Computer modeling of physical processes. Computer modeling"

COMPUTER SIMULATION(eng. computational simulation), construction using computers and computer devices(3D scanners, 3D printers, etc.) symbolic [see. Symbolic modeling(s-modeling)] and physical models of objects studied in science (physics, chemistry, etc.), created in technology (for example, in aircraft manufacturing, robotics), medicine (for example, in implantology, tomography), art (for example, ., in architecture, music) and other areas of human activity.

Computer modeling makes it possible to significantly reduce the cost of developing models in comparison with non-computer modeling methods and carrying out full-scale tests. It makes it possible to build symbolic computer models of objects for which it is impossible to build physical models (for example, models of objects studied in climatology). Serves as an effective means of modeling complex systems in technology, economics and other fields of activity. It is the technological basis of computer-aided design (CAD) systems.

Physical computer models are made on the basis of symbolic models and are prototypes of simulated objects (parts and assemblies of machines, building structures, etc.). To manufacture prototypes, 3D printers can be used that implement technologies for layer-by-layer formation of non-planar objects. Symbolic prototype models can be developed using CAD software, 3D scanners or digital cameras and photogrammetric software.

A computer system is a human-machine complex in which the construction of models is carried out using computer programs that implement mathematical (see. Mathematical modeling) and expert (eg, simulation) modeling methods. In the computational experiment mode, the researcher has the opportunity, by changing the initial data, to obtain and save in a computer modeling system a large number of variants of the object model in a relatively short time.

Clarification of ideas about the object under study and improvement of methods for its modeling may make it necessary to change the software of the computer modeling system, while the hardware may remain unchanged.

The high efficiency of computer modeling in science, technology and other fields of activity stimulates the development of hardware (including supercomputers) and software [including instrumental systems (see. Instrumental system in computer science) development of parallel programs for supercomputers].

These days, computer models are a rapidly growing part of the arsenal.

Mayer R.V. Computer simulation

Mayer R.V., Glazov Pedagogical Institute

COMPUTER SIMULATION:

MODELING AS A METHOD OF SCIENTIFIC KNOWLEDGE.

COMPUTER MODELS AND THEIR TYPES

The concept of a model is introduced, various classes of models are analyzed, and the connection between modeling and general systems theory is analyzed. Numerical, statistical and simulation modeling and its place in the system of other methods of cognition are discussed. Are being considered various classifications computer models and areas of their application.

1.1. The concept of a model. Modeling Goals

In the process of studying the surrounding world, the subject of knowledge is confronted with the studied part of objective reality –– object of knowledge. A scientist, using empirical methods of cognition (observation and experiment), establishes facts, characterizing the object. Elementary facts are summarized and formulated empirical laws. The next step is to develop the theory and construct theoretical model, which explains the behavior of the object and takes into account the most significant factors influencing the phenomenon being studied. This theoretical model must be logical and consistent with established facts. We can assume that any science is a theoretical model of a certain part of the surrounding reality.

Often in the process of cognition, a real object is replaced by some other ideal, imaginary or material object
, bearing the studied features of the object under study, and is called model. This model is subjected to research: it is subjected to various influences, parameters and initial conditions are changed, and it is found out how its behavior changes. The results of the model research are transferred to the research object, compared with available empirical data, etc.

Thus, a model is a material or ideal object that replaces the system under study and adequately reflects its essential aspects. The model must in some way repeat the process or object under study with a degree of correspondence that allows us to study the original object. In order for the simulation results to be transferred to the object under study, the model must have the property adequacy. The advantage of replacing the object under study with its model is that models are often easier, cheaper and safer to study. Indeed, in order to create an airplane, you need to build a theoretical model, draw a drawing, perform the appropriate calculations, make a small copy of it, study it in a wind tunnel, etc.

Object model should reflect its most important qualities, neglecting the secondary ones. Here it is appropriate to recall the parable of the three blind wise men who decided to find out what an elephant is. One wise man held an elephant by the trunk and said that the elephant is a flexible hose. Another touched the elephant's leg and decided that the elephant was a column. The third wise man pulled the tail and came to the conclusion that the elephant is a rope. It is clear that all the wise men were mistaken: none of the named objects (hose, column, rope) reflect the essential aspects of the object being studied (elephant), therefore their answers (proposed models) are not correct.

When modeling, various goals can be pursued: 1) knowledge of the essence of the object being studied, the reasons for its behavior, the “structure” and the mechanism of interaction of elements; 2) explanation of already known results of empirical studies, verification of model parameters using experimental data; 3) predicting the behavior of systems under new conditions under various external influences and control methods; 4) optimization of the functioning of the systems under study, search for the correct control of the object in accordance with the selected optimality criterion.

1.2. Various types models

The models used are extremely varied. System analysis requires classification and systematization, that is, structuring an initially unordered set of objects and turning it into a system. There are various ways to classify the existing variety of models. Thus, the following types of models are distinguished: 1) deterministic and stochastic; 2) static and dynamic; 3) discrete, continuous and discrete-continuous; 4) mental and real. In other works, models are classified on the following grounds (Fig. 1): 1) by the nature of the modeled side of the object; 2) in relation to time; 3) by the method of representing the state of the system; 4) according to the degree of randomness of the simulated process; 5) according to the method of implementation.

When classifying according to the nature of the modeled side of the object The following types of models are distinguished (Fig. 1): 1.1. Cybernetic or functional models; in them, the modeled object is considered as a “black box”, the internal structure of which is unknown. The behavior of such a “black box” can be described by a mathematical equation, graph or table that relates the output signals (reactions) of the device to the input signals (stimuli). The structure and operating principles of such a model have nothing in common with the object under study, but it functions in a similar way. For example, a computer program that simulates the game of checkers. 1.2. Structural models– these are models whose structure corresponds to the structure of the modeled object. Examples are tabletop exercises, self-government day, electronic circuit model in Electronics Workbench, etc. 1.3. Information models, representing a set of specially selected quantities and their specific values that characterize the object under study. There are verbal (verbal), tabular, graphical and mathematical information models. For example, a student's information model may consist of grades for exams, tests, and laboratory work. Or an information model of some production represents a set of parameters characterizing the needs of production, its most essential characteristics, and the parameters of the product being produced.

In relation to time highlight: 1. Static models–– models whose condition does not change over time: a model of the development of a block, a model of a car body. 2. Dynamic models are functioning objects whose state is constantly changing. These include working models of an engine and generator, a computer model of population development, an animated model of computer operation, etc.

By way of representing the system state distinguish: 1. Discrete models– these are automata, that is, real or imaginary discrete devices with a certain set of internal states that convert input signals into output signals in accordance with given rules. 2. Continuous models– these are models in which continuous processes occur. For example, the use of an analog computer to solve a differential equation, simulate radioactive decay using a capacitor discharging through a resistor, etc. According to the degree of randomness of the simulated process isolated (Fig. 1): 1. Deterministic models, which tend to move from one state to another in accordance with a rigid algorithm, that is, there is a one-to-one correspondence between the internal state, input and output signals (traffic light model). 2. Stochastic models, functioning like probabilistic automata; the output signal and the state at the next time are specified by a probability matrix. For example, a probabilistic model of a student, a computer model of message transmission over a communication channel with noise, etc.

Rice. 1. Various ways to classify models.

By implementation method distinguish: 1. Abstract models, that is, mental models that exist only in our imagination. For example, the structure of an algorithm, which can be represented using a block diagram, a functional dependence, a differential equation that describes a certain process. Abstract models also include various graphic models, diagrams, structures, and animations. 2. Material (physical) models They are stationary models or operating devices that function somewhat similar to the object under study. For example, a model of a molecule made of balls, a model of a nuclear submarine, a working model of an alternating current generator, an engine, etc. Real modeling involves building a material model of an object and performing a series of experiments with it. For example, to study the movement of a submarine in water, a smaller copy of it is built and the flow is simulated using a hydrodynamic tube.

We will be interested in abstract models, which in turn are divided into verbal, mathematical and computer. TO verbal or text models refer to sequences of statements in natural or formalized language that describe the object of cognition. Mathematical models form a wide class of iconic models that use mathematical operations and operators. Often they represent a system of algebraic or differential equations. Computer models are an algorithm or computer program that solves a system of logical, algebraic or differential equations and simulates the behavior of the system under study. Sometimes mental simulation is divided into: 1. Visual,–– involves the creation of an imaginary image, a mental model, corresponding to the object under study based on assumptions about the ongoing process, or by analogy with it. 2. symbolic,–– consists in creating a logical object based on a system of special characters; is divided into linguistic (based on the thesaurus of basic concepts) and symbolic. 3. Mathematical,–– consists in establishing correspondence to the object of study of some mathematical object; divided into analytical, simulation and combined. Analytical modeling involves writing a system of algebraic, differential, integral, finite-difference equations and logical conditions. To study the analytical model can be used analytical method and numerical method. Recently, numerical methods have been implemented on computers, so computer models can be considered as a type of mathematical ones.

Mathematical models are quite diverse and can also be classified on different grounds. By degree of abstraction when describing system properties they are divided into meta-, macro- and micro-models. Depending on presentation forms There are invariant, analytical, algorithmic and graphical models. By the nature of the displayed properties object models are classified into structural, functional and technological. By method of obtaining distinguish between theoretical, empirical and combined. Depending on character mathematical apparatus models can be linear and nonlinear, continuous and discrete, deterministic and probabilistic, static and dynamic. By way of implementation There are analogue, digital, hybrid, neuro-fuzzy models, which are created on the basis of analogue, digital, hybrid computers and neural networks.

1.3. Modeling and systems approach

The modeling theory is based on general systems theory, also known as systematic approach. This is a general scientific direction, according to which the object of research is considered as a complex system interacting with the environment. An object is a system if it consists of a set of interconnected elements, the sum of whose properties are not equal to the properties of the object. A system differs from a mixture by the presence of an ordered structure and certain connections between elements. For example, a TV set consisting of a large number of radio components connected to each other in a certain way is a system, but the same radio components lying randomly in a box are not a system. There are the following levels of description of systems: 1) linguistic (symbolic); 2) set-theoretic; 3) abstract-logical; 4) logical-mathematical; 5) information-theoretic; 6) dynamic; 7) heuristic.

Rice. 2. System under study and environment.

The system interacts with the environment, exchanges matter, energy, and information with it (Fig. 2). Each of its elements is subsystem. A system that includes the analyzed object as a subsystem is called supersystem. We can assume that the system has inputs, to which signals are received, and exits, issuing signals on Wednesday. Treating the object of cognition as a whole, made up of many interconnected parts, allows you to see something important behind a huge number of insignificant details and features and formulate system-forming principle. If the internal structure of the system is unknown, then it is considered a “black box” and a function is specified that links the states of the inputs and outputs. This is cybernetic approach. At the same time, the behavior of the system under consideration, its response to external influences and environmental changes are analyzed.

The study of the composition and structure of the object of cognition is called system analysis. His methodology is expressed in the following principles: 1) the principle physicality: the behavior of the system is described by certain physical (psychological, economic, etc.) laws; 2) principle modelability: the system can be modeled in a finite number of ways, each of which reflects its essential aspects; 3) principle focus: the functioning of fairly complex systems leads to the achievement of a certain goal, state, preservation of the process; at the same time, the system is able to withstand external influences.

As stated above, the system has structure – a set of internal stable connections between elements, determining the basic properties of a given system. It can be represented graphically in the form of a diagram, a chemical or mathematical formula, or a graph. This graphic image characterizes the spatial arrangement of elements, their nesting or subordination, the chronological sequence of various parts of a complex event. When building a model, it is recommended to draw up structural diagrams of the object being studied, especially if it is quite complex. This allows us to understand the totality of all integrative properties of an object that its constituent parts do not possess.

One of the most important ideas systematic approach is emergence principle, –– when elements (parts, components) are combined into a single whole, a systemic effect occurs: the system acquires qualities that none of its constituent elements possesses. The principle of highlighting the main structure system is that the study of a fairly complex object requires highlighting a certain part of its structure, which is the main or fundamental one. In other words, there is no need to take into account all the variety of details, but one should discard the less significant and enlarge the important parts of the object in order to understand the main patterns.

Any system interacts with other systems that are not part of it and form the environment. Therefore, it should be considered as a subsystem of some larger system. If we limit ourselves to analyzing only internal connections, then in some cases it will not be possible to create correct model object. It is necessary to take into account the essential connections of the system with the environment, that is external factors, and thereby “close” the system. This is principle of closure.

The more complex the object under study, the more different models (descriptions) can be built. Thus, looking at a cylindrical column from different sides, all observers will say that it can be modeled as a homogeneous cylindrical body of certain dimensions. If, instead of a column, observers begin to look at some complex architectural composition, then everyone will see something different and build their own model of the object. In this case, as in the case of the sages, various results will be obtained that contradict each other. And the point here is not that there are many truths or that the object of knowledge is fickle and many-sided, but that the object is complex and the truth is complex, and the methods of knowledge used are superficial and did not allow us to fully understand the essence.

When studying large systems, we start from principle of hierarchy, which is as follows. The object under study contains several related subsystems of the first level, each of which is itself a system consisting of subsystems of the second level, etc. Therefore, the description of the structure and the creation of a theoretical model must take into account the “location” of elements at various “levels,” that is, their hierarchy. The main properties of the systems include: 1) integrity, that is, the irreducibility of the properties of the system to the sum of the properties of individual elements; 2) structure, – heterogeneity, the presence of a complex structure; 3) plurality of description, –– the system can be described in various ways; 4) interdependence of system and environment, –– elements of the system are connected with objects that are not part of it and form the environment; 5) hierarchy, –– the system has a multi-level structure.

1.4. Qualitative and quantitative models

The task of science is to build a theoretical model of the surrounding world that would explain known and predict unknown phenomena. The theoretical model can be qualitative or quantitative. Let's consider quality explanation of electromagnetic oscillations in an oscillatory circuit consisting of a capacitor and an inductor. When a charged capacitor is connected to an inductor, it begins to discharge, and current, energy, flows through the inductor electric field transforms into magnetic field energy. When the capacitor is completely discharged, the current through the inductor reaches maximum value. Due to the inertia of the inductor, caused by the phenomenon of self-induction, the capacitor is recharged, it is charged in the opposite direction, etc. This qualitative model of the phenomenon makes it possible to analyze the behavior of the system and predict, for example, that when the capacitance of the capacitor decreases, the natural frequency of the circuit will increase.

An important step on the path of knowledge is transition from qualitative-descriptive methods to mathematical abstractions. The solution to many problems in natural science required the digitization of space and time, the introduction of the concept of a coordinate system, the development and improvement of methods for measuring various physical, psychological and other quantities, which made it possible to operate with numerical values. As a result, quite complex mathematical models were obtained, representing a system of algebraic and differential equations. Currently, the study of natural and other phenomena is no longer limited to qualitative reasoning, but involves the construction of a mathematical theory.

Creation quantitative models of electromagnetic oscillations in an RLC circuit involves the introduction of accurate and unambiguous methods for determining and measuring quantities such as current , charge , voltage , capacity , inductance , resistance . Without knowing how to measure the current in a circuit or the capacitance of a capacitor, it is pointless to talk about any quantitative relationships. Having unambiguous definitions of the listed quantities, and having established the procedure for their measurement, you can begin to build a mathematical model and write a system of equations. The result is a second-order inhomogeneous differential equation. Its solution allows, knowing the charge of the capacitor and the current through the inductor at the initial moment, to determine the state of the circuit at subsequent moments of time.

The construction of a mathematical model requires the determination of independent quantities that uniquely describe state the object under study. For example, the state of a mechanical system is determined by the coordinates of the particles entering it and the projections of their impulses. The state of the electrical circuit is determined by the charge of the capacitor, the current through the inductor, etc. State economic system determined by a set of indicators such as the number cash, invested in production, profit, number of workers engaged in manufacturing products, etc.

The behavior of an object is largely determined by its parameters, that is, quantities that characterize its properties. Thus, the parameters of a spring pendulum are the stiffness of the spring and the mass of the body suspended from it. The electrical RLC circuit is characterized by the resistance of the resistor, the capacitance of the capacitor, and the inductance of the coil. The parameters of a biological system include the reproduction rate, the amount of biomass consumed by one organism, etc. Another important factor influencing the behavior of an object is external influence. It is obvious that the behavior of a mechanical system depends on the external forces acting on it. The processes in the electrical circuit are affected by the applied voltage, and the development of production is associated with the external economic situation in the country. Thus, the behavior of the object under study (and therefore its model) depends on its parameters, initial state and external influence.

Creating a mathematical model requires determining the set of states of the system, a set of external influences ( input signals) and responses (output signals), as well as setting relationships connecting the system response with the impact and its internal state. They allow you to study a huge number of different situations, setting other system parameters, initial conditions and external influences. The required function characterizing the response of the system is obtained in tabular or graphical form.

All existing methods studies of the mathematical model can be divided into two groups .Analytical solving an equation often involves cumbersome and complex mathematical calculations and, as a result, leads to an equation expressing the functional relationship between the desired quantity, system parameters, external influences and time. The results of such a solution require interpretation, which involves analyzing the obtained functions and constructing graphs. Numerical methods research of a mathematical model on a computer involves the creation of a computer program that solves a system of corresponding equations and displays a table or graphic image. The resulting static and dynamic pictures clearly explain the essence of the processes under study.

1.5. Computer simulation

An effective way to study the phenomena of the surrounding reality is scientific experiment, consisting in reproducing the studied natural phenomenon under controlled and controlled conditions. However, often carrying out an experiment is impossible or requires too much economic effort and can lead to undesirable consequences. In this case, the object under study is replaced computer model and study its behavior under various external influences. Ubiquitous personal computers, information technology, the creation of powerful supercomputers has made computer modeling one of the effective methods for studying physical, technical, biological, economic and other systems. Computer models are often simpler and more convenient to study; they make it possible to carry out computational experiments, the real implementation of which is difficult or may give an unpredictable result. The logic and formalization of computer models makes it possible to identify the main factors that determine the properties of the objects under study and to study the response of a physical system to changes in its parameters and initial conditions.

Computer modeling requires abstracting from the specific nature of phenomena, building first a qualitative and then a quantitative model. This is followed by a series of computational experiments on a computer, interpretation of the results, comparison of modeling results with the behavior of the object under study, subsequent refinement of the model, etc. Computational experiment in fact, it is an experiment on a mathematical model of the object under study, carried out using a computer. It is often much cheaper and more accessible than a full-scale experiment, its implementation requires less time, and it provides more detailed information about the quantities characterizing the state of the system.

Essence computer modeling system consists in creating a computer program (software package) that describes the behavior of the elements of the system under study during its operation, taking into account their interaction with each other and the external environment, and conducting a series of computational experiments on a computer. This is done with the aim of studying the nature and behavior of the object, its optimization and structural development, and predicting new phenomena. Let's list t requirements, which the model of the system under study must satisfy: 1. Completeness models, that is, the ability to calculate all characteristics of the system with the required accuracy and reliability. 2. Flexibility models, which allows you to reproduce and play out various situations and processes, change the structure, algorithms and parameters of the system under study. 3. Duration of development and implementation, characterizing the time spent on creating the model. 4. Block structure, allowing the addition, exclusion and replacement of some parts (blocks) of the model. Besides, information support, software and hardware must allow the model to exchange information with the corresponding database and ensure efficient machine implementation and user-friendly operation.

To the main stages of computer modeling include (Fig. 3): 1) problem statement, description of the system under study and identification of its components and elementary acts of interaction; 2) formalization, that is, the creation of a mathematical model, which is a system of equations and reflects the essence of the object under study; 3) algorithm development, the implementation of which will solve the problem; 4) writing a program in a specific programming language; 5) planning And performing calculations on a computer, finalizing the program and obtaining results; 6) analysis And interpretation of results, their comparison with empirical data. Then all this is repeated at the next level.

Development computer model object is a sequence of iterations: first, based on the available information about the system S, a model is built
, a series of computational experiments is carried out, the results are analyzed. When receiving new information about an object S, additional factors are taken into account, and a model is obtained
, whose behavior is also studied on a computer. After this, models are created
,
etc. until a model is obtained that corresponds to the system S with the required accuracy.

Rice. 3. Stages of computer modeling.

In general, the behavior of the system under study is described by the law of functioning, where
–– vector of input influences (stimuli),
–– vector of output signals (responses, reactions),
–– vector of environmental influences,
–– vector of system eigenparameters. The operating law can take the form of a verbal rule, table, algorithm, function, set of logical conditions, etc. In the case when the law of functioning contains time, we talk about dynamic models and systems. For example, acceleration and braking asynchronous motor, transient process in a circuit containing a capacitor, operation of a computer network, queuing system. In all these cases, the state of the system, and hence its model, changes over time.

If the behavior of the system is described by the law
, not containing time obviously, we are talking about static models and systems, solving stationary problems, etc. Let's give a few examples: calculating a nonlinear direct current circuit, finding a stationary temperature distribution in a rod at constant temperatures of its ends, the shape of an elastic film stretched over a frame, the velocity profile in a steady flow of a viscous fluid, etc.

The functioning of the system can be considered as a sequential change of states
,
, … ,
, which correspond to some points in the multidimensional phase space. Set of all points
, corresponding to all possible states of the system, are called object state space(or models). Each implementation of the process corresponds to one phase trajectory passing through some points from the set . If a mathematical model contains an element of randomness, then a stochastic computer model is obtained. In a particular case, when the system parameters and external influences uniquely determine the output signals, we speak of a deterministic model.

Principles of computer modeling. Connection with other methods of cognition

So, A model is an object that replaces the system under study and imitates its structure and behavior. A model can be a material object, a set of data ordered in a special way, a system of mathematical equations or a computer program. Modeling is understood as the representation of the main characteristics of the object of study using another system (material object, set of equations, computer program). Let us list the principles of modeling:

1. Principle of adequacy: The model must take into account the most significant aspects of the object under study and reflect its properties with acceptable accuracy. Only in this case can the simulation results be extended to the object of study.

2. The principle of simplicity and economy: The model must be simple enough for its use to be effective and cost-effective. It should not be more complex than is required for the researcher.

3. The principle of information sufficiency: In the complete absence of information about the object, it is impossible to build a model. If complete information is available, modeling is meaningless. There is a level of information sufficiency, upon reaching which a model of the system can be built.

4. Feasibility principle: The created model must ensure the achievement of the stated research goal in a finite time.

5. The principle of plurality and unity of models: Any specific model reflects only some aspects of the real system. For a complete study, it is necessary to build a number of models that reflect the most significant aspects of the process under study and have something in common. Each subsequent model should complement and clarify the previous one.

6. Systematic principle. The system under study can be represented as a set of subsystems interacting with each other, which are modeled by standard mathematical methods. Moreover, the properties of the system are not the sum of the properties of its elements.

7. Principle of parameterization. Some subsystems of the modeled system can be characterized by a single parameter (vector, matrix, graph, formula).

The model must satisfy the following requirements: 1) be adequate, that is, reflect the most essential aspects of the object under study with the required accuracy; 2) contribute to the solution of a certain class of problems; 3) be simple and understandable, based on a minimum number of assumptions and assumptions; 4) allow oneself to be modified and supplemented, to move on to other data; 5) be convenient to use.

The connection between computer modeling and other methods of cognition is shown in Fig. 4. The object of knowledge is studied by empirical methods (observation, experiment), established facts are the basis for constructing a mathematical model. The resulting system of mathematical equations can be studied analytical methods or using a computer - in this case we are talking about creating a computer model of the phenomenon being studied. A series of computational experiments or computer simulations is carried out, and the resulting results are compared with the results of an analytical study of the mathematical model and experimental data. The findings are taken into account to improve the methodology for experimental study of the research object, develop a mathematical model and improve the computer model. The study of social and economic processes differs only in the inability to fully use experimental methods.

Rice. 4. Computer modeling among other methods of cognition.

1.6. Types of computer models

By computer modeling in the broadest sense we will understand the process of creating and studying models using a computer. The following types of modeling are distinguished:

1. Physical modeling : A computer is part of an experimental setup or simulator; it receives external signals, carries out appropriate calculations and issues signals that control various manipulators. For example, a training model of an aircraft, which is a cockpit mounted on appropriate manipulators connected to a computer, which responds to the pilot’s actions and changes the tilt of the cockpit, instrument readings, view from the window, etc., simulating the flight of a real aircraft.

2. Dynamic or numerical modeling, which involves the numerical solution of a system of algebraic and differential equations using methods of computational mathematics and conducting a computational experiment under various system parameters, initial conditions and external influences. It is used to simulate various physical, biological, social and other phenomena: pendulum oscillations, wave propagation, population changes, populations of a given animal species, etc.

3. Simulation modeling consists of creating a computer program (or software package) that simulates the behavior of a complex technical, economic or other system on a computer with the required accuracy. Simulation modeling provides a formal description of the logic of functioning of the system under study over time, which takes into account the significant interactions of its components and ensures the conduct of statistical experiments. Object-oriented computer simulations are used to study the behavior of economic, biological, social and other systems, to create computer games, the so-called virtual world”, training programs and animations. For example, a model of a technological process, an airfield, a certain industry, etc.

4. Statistical modeling is used to study stochastic systems and consists of repeated testing followed by statistical processing of the resulting results. Such models make it possible to study the behavior of all kinds of queuing systems, multiprocessor systems, information and computer networks, various dynamic systems, which are influenced by random factors. Statistical models are used in solving probabilistic problems, as well as in processing large amounts of data (interpolation, extrapolation, regression, correlation, calculation of distribution parameters, etc.). They are different from deterministic models, the use of which involves the numerical solution of systems of algebraic or differential equations, or the replacement of the object under study with a deterministic automaton.

5. Information modeling consists in creating an information model, that is, a set of specially organized data (signs, signals) reflecting the most significant aspects of the object under study. There are visual, graphic, animation, text, and tabular information models. These include all kinds of diagrams, graphs, graphs, tables, diagrams, drawings, animations made on a computer, including a digital star map, a computer model of the earth's surface, etc.

6. Knowledge modeling involves the construction of an artificial intelligence system, which is based on the knowledge base of a certain subject area (part of the real world). Knowledge bases consist of facts(data) and rules. For example, a computer program that can play chess (Fig. 5) must operate with information about the “abilities” of various chess pieces and “know” the rules of the game. This type of model includes semantic networks, logical knowledge models, expert systems, logic games, etc. Logic models used to represent knowledge in expert systems, to create artificial intelligence systems, carry out logical inference, prove theorems, mathematical transformations, building robots, using natural language to communicate with computers, creating a virtual reality effect in computer games etc.

Rice. 5. Computer model of chess player behavior.

Based on modeling purposes, computer models are divided into groups: 1) descriptive models, used to understand the nature of the object being studied, identifying the most significant factors influencing its behavior; 2) optimization models, allowing you to select the best way management of a technical, socio-economic or other system (for example, a space station); 3) predictive models, helping to predict the state of an object at subsequent points in time (a model of the earth’s atmosphere that allows one to predict the weather); 4) training models, used for teaching, training and testing students, future specialists; 5) gaming models , allowing you to create a game situation that simulates control of an army, state, enterprise, person, airplane, etc., or playing chess, checkers and other logic games.

Classification of computer models

according to the type of mathematical scheme

In the theory of system modeling, computer models are divided into numerical, simulation, statistical and logical. In computer modeling, as a rule, one of the standard mathematical schemes is used: differential equations, deterministic and probabilistic automata, queuing systems, Petri nets, etc. Taking into account the method of representing the state of the system and the degree of randomness of the simulated processes allows us to construct Table 1.

Table 1.

According to the type of mathematical scheme, they are distinguished: 1 . Continuously determined models, which are used to model dynamic systems and involve solving a system of differential equations. Mathematical schemes This type is called D-schemes (from the English dynamic). 2. Discrete-deterministic models are used to study discrete systems that can be in one of many internal states. They are modeled by an abstract finite automata, specified by the F-scheme (from the English finite automata): . Here
, –– a variety of input and output signals, –– a variety of internal states,
–– transition function,
–– function of outputs. 3. Discrete-stochastic models involve the use of a scheme of probabilistic automata, the functioning of which contains an element of randomness. They are also called P-schemes (from the English probabilistic automat). The transitions of such an automaton from one state to another are determined by the corresponding probability matrix. 4. Continuous-stochastic models As a rule, they are used to study queuing systems and are called Q-schemes (from the English queuing system). For the functioning of some economic, industrial, technical systems inherent random occurrence of requirements (applications) for service and random service time. 5. Network models are used to analyze complex systems in which several processes occur simultaneously. In this case, they talk about Petri nets and N-schemes (from the English Petri Nets). The Petri net is given by a quadruple, where – many positions,
– many transitions, – input function, – output function. The labeled N-scheme allows you to simulate parallel and competing processes in various systems. 6. Combined schemes are based on the concept of an aggregate system and are called A-schemes (from the English aggregate system). This universal approach, developed by N.P. Buslenko, allows us to study all kinds of systems that are considered as a set of interconnected units. Each unit is characterized by vectors of states, parameters, environmental influences, input influences (control signals), initial states, output signals, transition operator, output operator.

The simulation model is studied using digital and analogue computers. The simulation system used includes mathematical, software, information, technical and ergonomic support. The effectiveness of simulation modeling is characterized by the accuracy and reliability of the resulting results, the cost and time of creating a model and working with it, and the cost of machine resources (computation time and required memory). To assess the effectiveness of the model, it is necessary to compare the resulting results with the results of a full-scale experiment, as well as the results of analytical modeling.

In some cases, it is necessary to combine the numerical solution of differential equations and simulation of the functioning of a particular rather complex system. In this case they talk about combined or analytical and simulation modeling. Its main advantage is the ability to study complex systems, take into account discrete and continuous elements, nonlinearity of various characteristics, and random factors. Analytical modeling allows you to analyze only fairly simple systems.

One of effective methods simulation model research is statistical test method. It involves repeated reproduction of a particular process with various parameters changing randomly according to a given law. A computer can conduct 1000 tests and record the main characteristics of the system’s behavior, its output signals, and then determine their mathematical expectation, dispersion, and distribution law. The disadvantage of using a machine implementation of a simulation model is that the solution obtained with its help is of a private nature and corresponds to specific parameters of the system, its initial state and external influences. The advantage is the ability to study complex systems.

1.8. Areas of application of computer models

The improvement of information technology has led to the use of computers in almost all areas of human activity. The development of scientific theories involves putting forward basic principles, constructing a mathematical model of the object of knowledge, and obtaining consequences from it that can be compared with the results of an experiment. The use of a computer allows, based on mathematical equations, to calculate the behavior of the system under study under certain conditions. Often this is the only way to obtain consequences from a mathematical model. For example, consider the problem of the motion of three or more particles interacting with each other, which is relevant when studying the motion of planets, asteroids and other celestial bodies. In the general case, it is complex and does not have an analytical solution, and only the use of computer modeling allows one to calculate the state of the system at subsequent points in time.

The improvement of computer technology, the emergence of a computer that allows one to quickly and accurately carry out calculations according to a given program, marked a qualitative leap in the development of science. At first glance, it seems that the invention of computers cannot directly influence the process of cognition of the surrounding world. However, this is not so: solving modern problems requires the creation of computer models, carrying out a huge number of calculations, which became possible only after the advent of electronic computers capable of performing millions of operations per second. It is also significant that calculations are performed automatically, in accordance with a given algorithm, and do not require human intervention. If a computer belongs to the technical basis for conducting a computational experiment, then its theoretical basis are applied mathematics, numerical methods for solving systems of equations.

The successes of computer modeling are closely related to the development of numerical methods, which began with the fundamental work of Isaac Newton, who back in the 17th century proposed using them for the approximate solution of algebraic equations. Leonhard Euler developed a method for solving ordinary differential equations. Among modern scientists, a significant contribution to the development of computer modeling was made by Academician A.A. Samarsky, the founder of the methodology of computational experiments in physics. It was they who proposed the famous triad “model – algorithm – program” and developed computer modeling technology, successfully used to study physical phenomena. One of the first outstanding results of a computer experiment in physics was the discovery in 1968 of a temperature current layer in the plasma created in MHD generators (T-layer effect). It was performed on a computer and made it possible to predict the outcome of a real experiment conducted several years later. Currently, the computational experiment is used to carry out research in the following areas: 1) calculation of nuclear reactions; 2) solving problems of celestial mechanics, astronomy and astronautics; 3) study of global phenomena on Earth, modeling of weather, climate, study of environmental problems, global warming, consequences of a nuclear conflict, etc.; 4) solving problems of continuum mechanics, in particular, hydrodynamics; 5) computer modeling of various technological processes; 6) calculation of chemical reactions and biological processes, development of chemical and biological technology; 7) sociological research, in particular, modeling elections, voting, dissemination of information, changes in public opinion, military operations; 8) calculation and forecasting of the demographic situation in the country and the world; 9) simulation modeling of the operation of various technical, in particular electronic devices; 10) economic research on the development of an enterprise, industry, country.

Literature

Boev V.D., Sypchenko R.P., Computer modeling. –– INTUIT.RU, 2010. –– 349 p. Bulavin L.A., Vygornitsky N.V., Lebovka N.I. Computer modeling of physical systems. –– Dolgoprudny: Publishing House “Intelligence”, 2011. – 352 p. Buslenko N.P. Modeling of complex systems. –– M.: Nauka, 1968. –– 356 p. Dvoretsky S.I., Muromtsev Yu.L., Pogonin V.A. Systems modeling. –– M.: Publishing house. Center “Academy”, 2009. –– 320 p. Kunin S. Computational physics. –– M.: Mir, 1992. –– 518 p. Panichev V.V., Solovyov N.A. Computer modeling: textbook. –– Orenburg: State Educational Institution OSU, 2008. – 130 p. Rubanov V.G., Filatov A.G. Modeling systems tutorial. –– Belgorod: BSTU Publishing House, 2006. –– 349 p. Samarsky A.A., Mikhailov A.P. Mathematical Modeling: Ideas. Methods. Examples. –– M.: Fizmatlit, 2001. –– 320 p. Sovetov B.Ya., Yakovlev S.A. Modeling of systems: Textbook for universities –– M.: Vyssh. School, 2001. – 343 p.

10. Fedorenko R.P. Introduction to computational physics: Proc. manual: For universities. –– M.: Publishing house Mosk. Phys.-Techn. Institute, 1994. –– 528 p.

11. Shannon R. Simulation modeling of systems: art and science. –– M.: Mir, 1978. –– 302 p.

Mayer R.V. COMPUTER SIMULATION: SIMULATION AS A METHOD OF SCIENTIFIC COGNITION. COMPUTER MODELS AND THEIR TYPES // Scientific electronic archive.
URL: (access date: 03/28/2019).

Let's start with the definition of the word modeling.

Modeling is the process of constructing and using a model. A model is understood as a material or abstract object that, in the process of study, replaces the original object, preserving its properties that are important for this study.

Computer modeling as a method of cognition is based on mathematical modeling. A mathematical model is a system of mathematical relationships (formulas, equations, inequalities and signed logical expressions) that reflect the essential properties of the object or phenomenon being studied.

It is very rarely possible to use a mathematical model for specific calculations without the use of computer technology, which inevitably requires the creation of some kind of computer model.

Let's look at the computer modeling process in more detail.

2.2. Introduction to Computer Modeling

Computer modeling is one of the effective methods for studying complex systems. Computer models are easier and more convenient to study due to their ability to conduct computational experiments in cases where real experiments are difficult due to financial or physical obstacles or may give unpredictable results. The logic of computer models makes it possible to identify the main factors that determine the properties of the original object under study (or an entire class of objects), in particular, to study the response of the simulated physical system to changes in its parameters and initial conditions.

Computer modeling as a new method of scientific research is based on:

1. Construction of mathematical models to describe the processes being studied;

2. Using the latest high-speed computers (millions of operations per second) and capable of conducting a dialogue with a person.

Distinguish analytical And imitation modeling. In analytical modeling, mathematical (abstract) models of a real object are studied in the form of algebraic, differential and other equations, as well as those involving the implementation of an unambiguous computational procedure leading to their exact solution. In simulation modeling, mathematical models are studied in the form of an algorithm that reproduces the functioning of the system under study by sequentially executing large quantity elementary operations.

2.3. Building a computer model

The construction of a computer model is based on abstraction from the specific nature of phenomena or the original object being studied and consists of two stages - first creating a qualitative and then a quantitative model. Computer modeling consists of conducting a series of computational experiments on a computer, the purpose of which is to analyze, interpret and compare the modeling results with the real behavior of the object under study and, if necessary, subsequent refinement of the model, etc.

So, The main stages of computer modeling include:

1. Statement of the problem, definition of the modeling object:

At this stage, information is collected, a question is formulated, goals are defined, forms for presenting results, and data is described.

2. System analysis and research:

system analysis, meaningful description of the object, development of an information model, analysis of hardware and software, development of data structures, development of a mathematical model.

3. Formalization, that is, the transition to a mathematical model, the creation of an algorithm:

choosing a method for designing an algorithm, choosing a form for writing an algorithm, choosing a testing method, designing an algorithm.

4. Programming:

choosing a programming language or application environment for modeling, clarifying ways to organize data, writing an algorithm in the selected programming language (or in an application environment).

5. Conducting a series of computational experiments:

debugging of syntax, semantics and logical structure, test calculations and analysis of test results, program modification.

6. Analysis and interpretation of results:

modification of the program or model if necessary.

There are many software packages and environments that allow you to build and study models:

Graphics environments

Text editors

Programming environments

Spreadsheets

Math packages

HTML editors

2.4. Computational experiment

An experiment is an experience that is performed with an object or model. It consists of performing certain actions to determine how the experimental sample reacts to these actions. A computational experiment involves carrying out calculations using a formalized model.

Using a computer model that implements a mathematical one is similar to conducting experiments with a real object, only instead of a real experiment with an object, a computational experiment is carried out with its model. By specifying a specific set of values of the initial parameters of the model, as a result of a computational experiment, a specific set of values of the required parameters is obtained, the properties of objects or processes are studied, and they are found optimal parameters and operating modes, specify the model. For example, having an equation that describes the course of a particular process, you can, by changing its coefficients, initial and boundary conditions, study how the object will behave. Moreover, it is possible to predict the behavior of an object under various conditions. To study the behavior of an object with a new set of initial data, it is necessary to conduct a new computational experiment.

To check the adequacy of the mathematical model and the real object, process or system, the results of computer research are compared with the results of an experiment on a prototype full-scale model. The test results are used to adjust the mathematical model or the question of the applicability of the constructed mathematical model to the design or study of specified objects, processes or systems is resolved.

A computational experiment allows you to replace an expensive full-scale experiment with computer calculations. It allows, in a short time and without significant material costs, to study a large number of options for a designed object or process for various modes of its operation, which significantly reduces the time required for the development of complex systems and their implementation in production.

2.5. Simulation in various environments

2.5.1. Simulation in a programming environment

Modeling in a programming environment includes the main stages of computer modeling. At the stage of building an information model and algorithm, it is necessary to determine which quantities are input parameters and which are results, and also determine the type of these quantities. If necessary, an algorithm is drawn up in the form of a block diagram, which is written in the selected programming language. After this, a computational experiment is carried out. To do this, you need to download the program to RAM computer and run it. A computer experiment necessarily includes an analysis of the results obtained, on the basis of which all stages of solving the problem (mathematical model, algorithm, program) can be adjusted. One of the most important stages is testing the algorithm and program.

Debugging a program (the English term debugging means “catching bugs” appeared in 1945, when electrical circuits one of the first Mark-1 computers was hit by a moth and blocked one of the thousands of relays) - this is the process of finding and eliminating errors in the program, carried out based on the results of a computational experiment. During debugging, localization and elimination occurs syntax errors and obvious coding errors.

In modern software systems debugging is carried out using special software tools called debuggers.

Testing is checking the correct operation of the program as a whole or its components. The testing process checks the functionality of the program and does not contain obvious errors.

No matter how carefully the program is debugged, the decisive stage that establishes its suitability for work is monitoring the program based on the results of its execution on the test system. A program can be considered correct if, for the selected system of test input data, correct results are obtained in all cases.

2.5.2. Modeling in Spreadsheets

Modeling in spreadsheets covers a very wide class of problems in different subject areas. Spreadsheets are a universal tool that allows you to quickly perform labor-intensive work on calculating and recalculating the quantitative characteristics of an object. When modeling using spreadsheets, the algorithm for solving the problem is somewhat transformed, hiding behind the need to develop a computing interface. The debugging stage is retained, including the elimination of data errors in connections between cells and in computational formulas. Additional tasks also arise: work on the convenience of presentation on the screen and, if it is necessary to output the received data on paper, on their placement on sheets.

The modeling process in spreadsheets follows a general pattern: goals are defined, characteristics and relationships are identified, and a mathematical model is compiled. The characteristics of the model are necessarily determined by purpose: initial (affecting the behavior of the model), intermediate, and what is required to be obtained as a result. Sometimes the representation of an object is supplemented with diagrams and drawings.

A computer model is natural. Computer modeling is used everywhere, making the design and production of real systems, machines, mechanisms, goods, products economical, practical, and effective. The results are always pre-simulated.

Man has always built models, but with the advent of computer technology, mathematical, computational and software methods raised the ideas and technologies of modeling to extraordinary heights, making them widely applicable: from the primitive technical level to the level of high art and creativity.

A computer model is not only a more advanced spacecraft or conceptual system to understand public consciousness, but also a real opportunity to assess climate change on the planet or determine the consequences of a comet impact in a few hundred years.

Technical Modeling

Today, few specialists do not know, and this program is already competing with a dozen more advanced solutions.

Modeling a modern airplane or bicycle ultimately requires not only the automation of the production of drawings and the preparation of documentation. The modeling program is required to do the technical part: draw up drawings and documentation - this is the foundation.

The program must also show a real product in real use in time in three-dimensional space: in flight, in motion, in use, including possible accidents, energy replacement, negative impacts of humans or nature, corrosion, climate or other circumstances.

System Modeling

A model of a machine, a product, a conveyor is a system, but a system of clear structure and content, already manufactured once. For each there is experience, knowledge and examples of using computer models.

Technical reality is the same system as the system of relations in society, a system advertising campaign, a model of the human psyche or its circulatory system.

For example, a reliable diagnosis of a disease today can be obtained as:

the result of the competent actions of the doctor;
output of a computer program that built a model of the patient's condition.

These two options increasingly lead to the same result.

Man lives in a world of systems, and these systems require decisions that require initial data: understanding and perception of the surrounding reality. Without modeling it is impossible to understand the nature of systems and make decisions.

Only a computer mathematical model makes it possible to evaluate the objectivity and level of understanding of the original system, gradually bringing the created virtual image closer to the original.

Abstraction in Modeling

Computer models and simulation are an extremely promising and dynamically developing area of technology. Here, high-tech solutions are a common (ordinary, daily) event, and the possibilities of models and simulations amaze any sophisticated imagination.

However, people have not yet reached abstract system modeling. Examples of the use of computer models are real examples of real systems. For each direction of modeling, for each type of model, each type of product, conveyor, etc. there is its own separate program or its own separate item in the menu of a program that provides modeling in a relatively wide range of systems.

Software tools themselves are models. The result of a programmer's work is always a model. Whether a program is good or bad, it is always a model for solving a specific problem, which receives initial data and generates a result.

Classical programming - classic models, no abstraction: an exact task without variations in dynamics after its development is completed. It's like a real machine, a real product, any product with strict quantitative and qualitative characteristics: done - use it within the limits of what is available, but nothing beyond what is done.

Object-oriented programming - system model with a claim to abstraction and dynamics of structure and properties, that is, with an orientation towards the creation of a dynamic model that determines its purpose by the environment of application or the problem being solved.

Here the model can “live” after it finds itself in the application area alone without its creator (author) and will independently “collaborate” with users.

Modeling: the essence of the process

The concept of a computer model today is represented by different versions of opinions, but they all agree that the work of a program, and in context: the model is equal to the result of the actions of a specialist who works in a specific modeling environment of a particular program.

There are three types of models: cognitive, pragmatic and instrumental.

In the first case, the modeling aspect is expressed most of all as the desire to obtain a model in the format of the embodiment of knowledge, knowledge of theory, and a global process. Pragmatic model - gives an idea of practical actions, a worker, a production management system, a product, a machine. The third option is understood as an environment for constructing, analyzing and testing all models in general.

Typically, computer modeling is the activity of a specialist in constructing and studying a material or ideal (virtual) object that replaces the system under study, but adequately reflects its essential aspects, qualitative and quantitative characteristics.

Species diversity of simulated systems

In the field of modeling, as in all advanced areas of high technology, science, engineering and programming, there are many opinions on the classification and definition of the variety of types of systems being modeled.

But experts and specialists always agree on one thing: the types of computer models can be determined by objective points:

time;
method of presentation;
the nature of the modeled party;
level of uncertainty;
implementation option.

The time point is static and dynamic models. The first ones can be refined as much as you like, but dynamic models develop, and they are different at each moment in time. The mode of representation is usually understood as either discrete or continuous. The nature of the modeled side is informational, structural or functional (cybernetic).

The introduction of uncertainty parameters into the modeled system in many cases is not only justified, but is also a consequence of scientific achievements in related fields of knowledge. For example, building a climate model in a certain geographic region will not be feasible without many stochastic factors.

Modern modeling tools

Modeling today is a huge experience of many decades of development of the computer industry, which has represented many centuries of modeling, in general, and mathematical modeling, in particular, in the form of algorithms and programs.

Popular software tools are represented by a small family of widely known products: AutoCAD, 3D Max, Wings 3D, Blender 3D, SketchUp. There are many custom implementations based on these products.

In addition to the known, there is a significant private one, for example, the market for geographical, cartographic, geodetic; market of the film and video industry, represented by a significant number of little-known software products. The GeoSoft, TEPLOV, Houdini, etc. families in their field of competence are few inferior to others in quality, usefulness and efficiency.

When choosing the best software tool, the best solution is to evaluate the area of the intended modeling, the environment of existence of the future model. This will allow you to decide on the necessary tools.

Small and creative models

And although there is “little creativity left” in the design of a modern airbus, sports car or spaceship, in fact, programming and organizing business processes have become the subject of the closest attention and the target for the most expensive and complex modeling processes.

Modern business is not only hundreds of employees and pieces of equipment, but also thousands of production and social connections inside and outside the company. This is a completely new and unexplored direction: cloud technologies, organization of privileged access, protection from malicious attacks, unlawful action of an employee.

Modern programming has become too complex and has become a special kind of programming that has a life of its own. A software product created by one team of developers is intended to be modeled and studied for another company of developers.

Authoritative example

You can imagine a Windows system or a Linux family as a subject of modeling and get someone to build adequate models. The practical significance here is so low that it is cheaper to just work and not pay attention to the shortcomings of these systems. Their developer has his own idea of the development path he needs, and is not going to deviate from it.

With regard to databases and the dynamics of their development, the opposite can be said. Oracle - large company. Many ideas, thousands of developers, hundreds of thousands of solutions brought to perfection.

But Oracle is the foundation and powerful reason for modeling in the first place, and it appears that investing in this process will have a tremendous return on investment.

Oracle took the lead from the very beginning and was not inferior to anyone in the field of creating databases, ensuring a responsible attitude towards information, its protection, migration, storage, etc. Everything that is required for service information tasks, is Oracle.

The Downside of Oracle

Investments and work of the best developers to solve a pressing problem are an objective necessity. Over the many decades of its leadership, Oracle has completed hundreds of urgent tasks, and thousands of implementations and updates.

The sphere of information in the context of computer applications has not changed from the 80s to this day. Conceptually, the databases of the beginning of the computer era and today are twin brothers with differences in the level of security and implemented functionality.

To achieve the current level of “security and implemented functionality,” Oracle performed, in particular:

compatibility of large flows of heterogeneous information;
data migration and transformation;
application verification and testing;
generalized relational functionality for universal access;
migration of data/specialists;
transformation of the fundamental principles of corporate databases into a distributed Internet environment;
maximum integration, aggregators, systematization;
determining the range of feasibility, eliminating duplicative processes.

This is only a small fraction of the topics that make up multi-volume descriptions of existing software products from Oracle. In fact, the range of manufactured solutions is much wider and more powerful. All of them are supported by Oracle and thousands of qualified specialists.

Income model

If in the 80s Oracle had gone through modeling, rather than concrete capacity building in the form of real, complete solutions, the situation would have turned out significantly differently. By and large, a person or an enterprise does not need much from a computer information system. Here the study of the computer model is not of interest.

You always need to get only a solution to the problem that has arisen. How this decision is obtained is never of concern to the consumer. He is completely uninterested in knowing what data migration is or how to test the application code so that it works on any data, and in case of an unforeseen situation he can calmly report it and not do it blue screen or hang silently.

By modeling the next need programmatically, rather than by investing in yet another specialist who will apply his intelligence and knowledge to create the next piece of code, more can be achieved.

Any, the best specialist is, first of all, a static code, it is a recording of the best knowledge in the format of a monument to the author. It's just code. The result of the work of the best does not develop, but for its development it requires new developers, new authors.

Probability of implementing an income model

Developers and the IT industry as a whole have stopped treating dynamics, knowledge and artificial intelligence with the enthusiasm that accompanied the waves of interest of previous years.

Purely formally, many associate their products or areas of work with the topic of artificial intelligence, but, in fact, they are engaged in the implementation of strictly defined algorithms, cloud solutions, attach importance to security and protection from all kinds of threats.

Meanwhile, the computer model is dynamics. Computer modeling is its consequences. This objective circumstance has not yet been canceled. It is completely impossible to cancel it. The example of Oracle shows in the best possible way and more indicative than others how labor-intensive, expensive and ineffective it is to engage in forced modeling, when you have to build really working models with the labor of many thousands of specialists, and not automatically using the means of the designed information system itself - models in dynamics in real practice!

Let's start with the definition of the word modeling.

It is very rarely possible to use a mathematical model for specific calculations without the use of computer technology, which inevitably requires the creation of some kind of computer model.

Let's look at the computer modeling process in more detail.

2.2. Introduction to Computer Modeling

Computer modeling as a new method of scientific research is based on:

1. Construction of mathematical models to describe the processes being studied;

2. Using the latest high-speed computers (millions of operations per second) and capable of conducting a dialogue with a person.

2.3. Building a computer model

So, The main stages of computer modeling include:

1. Statement of the problem, definition of the modeling object:

At this stage, information is collected, a question is formulated, goals are defined, forms for presenting results, and data is described.

2. System analysis and research:

system analysis, meaningful description of the object, development of an information model, analysis of hardware and software, development of data structures, development of a mathematical model.

3. Formalization, that is, the transition to a mathematical model, the creation of an algorithm:

choosing a method for designing an algorithm, choosing a form for writing an algorithm, choosing a testing method, designing an algorithm.

4. Programming:

5. Conducting a series of computational experiments:

debugging of syntax, semantics and logical structure, test calculations and analysis of test results, program modification.

6. Analysis and interpretation of results:

modification of the program or model if necessary.

There are many software packages and environments that allow you to build and study models:

Graphics environments

Text editors

Programming environments

Spreadsheets

Math packages

HTML editors

2.4. Computational experiment

Using a computer model that implements a mathematical one is similar to conducting experiments with a real object, only instead of a real experiment with an object, a computational experiment is carried out with its model. By specifying a specific set of values for the initial parameters of the model, as a result of a computational experiment, a specific set of values for the required parameters is obtained, the properties of objects or processes are studied, their optimal parameters and operating modes are found, and the model is refined. For example, having an equation that describes the course of a particular process, you can, by changing its coefficients, initial and boundary conditions, study how the object will behave. Moreover, it is possible to predict the behavior of an object under various conditions. To study the behavior of an object with a new set of initial data, it is necessary to conduct a new computational experiment.

2.5. Simulation in various environments

2.5.1. Simulation in a programming environment

Modeling in a programming environment includes the main stages of computer modeling. At the stage of building an information model and algorithm, it is necessary to determine which quantities are input parameters and which are results, and also determine the type of these quantities. If necessary, an algorithm is drawn up in the form of a block diagram, which is written in the selected programming language. After this, a computational experiment is carried out. To do this, you need to load the program into the computer's RAM and run it for execution. A computer experiment necessarily includes an analysis of the results obtained, on the basis of which all stages of solving the problem (mathematical model, algorithm, program) can be adjusted. One of the most important stages is testing the algorithm and program.

Debugging a program (the English term debugging means “catching bugs” appeared in 1945, when a moth got into the electrical circuits of one of the first Mark-1 computers and blocked one of thousands of relays) is the process of finding and eliminating errors in the program , are produced based on the results of a computational experiment. Debugging involves localizing and eliminating syntax errors and obvious coding errors.

In modern software systems, debugging is carried out using special software tools called debuggers.

Testing is checking the correct operation of the program as a whole or its components. The testing process checks the functionality of the program and does not contain obvious errors.

2.5.2. Modeling in Spreadsheets

To visually display the dependence of the calculation results on the initial data, charts and graphs are used.

Testing uses a certain set of data for which the exact or approximate result is known. The experiment consists of introducing input data that satisfies the modeling goals. Analysis of the model will make it possible to find out how well the calculations meet the modeling goals.

2.5.3. Modeling in a DBMS environment

Modeling in a DBMS environment usually pursues the following goals:

Storing information and editing it in a timely manner;

Organizing data according to certain criteria;

Creation of various data selection criteria;

Convenient presentation of selected information.

In the process of developing the model, the structure of the future database is formed based on the initial data. The described characteristics and their types are summarized in a table. The number of table columns is determined by the number of object parameters (table fields). The number of rows (table records) corresponds to the number of rows of described objects of the same type. A real database may have not one, but several tables interconnected. These tables describe the objects included in a certain system. After defining and specifying the structure of the database in the computer environment, they proceed to filling it.

During the experiment, data is sorted, searched and filtered, and calculation fields are created.

A computer information panel provides the ability to create various screen forms and forms for displaying information in printed form - reports. Each report contains information relevant to the purpose of the particular experiment. It allows you to group information according to specified characteristics, in any order, with the introduction of final calculation fields.

If the results obtained do not correspond to the planned ones, you can conduct additional experiments by changing the conditions for sorting and searching for data. If there is a need to change the database, you can adjust its structure: change, add and delete fields. The result is a new model.

2.6. Using a computer model

Computer modeling and computational experiment as a new method of scientific research makes it possible to improve the mathematical apparatus used in constructing mathematical models, allowing, using mathematical methods, clarify, complicate mathematical models. The most promising for conducting a computational experiment is its use for solving major scientific, technical and socio-economic problems of our time, such as the design of reactors for nuclear power plants, the design of dams and hydroelectric power plants, magnetohydrodynamic energy converters, and in the field of economics - drawing up a balanced plan for the industry, region, country, etc.

In some processes where a natural experiment is dangerous to human life and health, a computational experiment is the only possible one (thermonuclear fusion, space exploration, design and research of chemical and other industries).

2.7. Conclusion

In conclusion, it can be emphasized that computer modeling and computational experiment make it possible to reduce the study of a “non-mathematical” object to the solution of a mathematical problem. This opens up the possibility of using a well-developed mathematical apparatus in combination with powerful computing technology to study it. This is the basis for the use of mathematics and computers to understand the laws of the real world and use them in practice.

3. List of references used

1. S. N. Kolupaeva. Mathematical and computer modeling. Study guide. – Tomsk, School University, 2008. – 208 p.

2. A. V. Mogilev, N. I. Pak, E. K. Henner. Informatics. Study guide. – M.: Center “Academy”, 2000. – 816 p.

3. D. A. Poselov. Informatics. Encyclopedic Dictionary. – M.: Pedagogika-Press, 1994. 648 p.

4. Official website of the publishing house "Open Systems". Internet University of Information Technologies. – Access mode: http://www.intuit.ru/. Date of access: October 5, 2010