Computer modeling in physics. Concept of computer simulation

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 using computer technology, which inevitably requires the creation of some 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 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. Logic computer models allows us 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 how new method scientific research is based on:

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

2. Using the latest computers, with high performance (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. Simulation modeling examines mathematical models 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:

on 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 information model, analysis of technical 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 ​​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.

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 design or research is resolved given objects, processes or systems.

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 of calculation and recalculation quantitative characteristics 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 spreadsheet modeling process is performed using general scheme: 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.

To visually display the dependence of 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 database structure in computer environment 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 scientific research forces to improve the mathematical apparatus used in constructing mathematical models, allows, 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 a solution mathematical problem. This opens up the possibility of using a well-developed mathematical apparatus combined with powerful computer technology. 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

Or a set of interacting computers (computing nodes), implementing a representation of an object, system or concept in a form different from the real one, but close to the algorithmic description, including a set of data characterizing the properties of the system and the dynamics of their change over time.

Encyclopedic YouTube

1 / 3

✪ 3D modeling programs for beginners. Part two

✪ Computer clothing modeling program InvenTexStudio 2010

✪ Computer programs in design work: what they are and why they are needed

Subtitles

About computer modeling

Computer models have become a common tool for mathematical modeling and are used in physics, astrophysics, mechanics, chemistry, biology, economics, sociology, meteorology, other sciences and applied problems in various fields of radio electronics, mechanical engineering, automotive industry, etc. Computer models are used to obtain new knowledge about an object or to approximate the behavior of systems that are too complex for analytical study.

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 carry out the so-called. computational experiments, in cases where real experiments are difficult due to financial or physical obstacles or may give unpredictable results. The logic and formalization of computer models makes it possible to determine 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.

The construction of a computer model is based on abstraction from the specific nature of the phenomena or the original object being studied and consists of two stages - first the creation of a qualitative and then a quantitative model. The more significant properties are identified and transferred to the computer model, the closer it will be to the real model, the greater the capabilities a system using this 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.

There are analytical and simulation 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(s) that reproduces the functioning of the system under study by sequentially performing a large number of elementary operations.

Advantages of computer modeling

Computer modeling makes it possible to:

• expand the range of research objects - it becomes possible to study non-repeating phenomena, phenomena of the past and future, objects that are not reproduced in real conditions;
• visualize objects of any nature, including abstract ones;
• explore phenomena and processes in the dynamics of their deployment;
• control time (speed up, slow down, etc.);
• perform repeated tests of the model, each time returning it to its original state;
• receive different characteristics object in numerical or graphical form;
• find the optimal design of an object without making trial copies;
• conduct experiments without risk of negative consequences for human health or the environment.

Main stages of computer modeling

During the process of conducting an experiment, it may become clear that you need:

• adjust the research plan;
• choose a different method for solving the problem;
• improve the algorithm for obtaining results;
• clarify the information model;
• make changes to the problem statement.

In this case, a return to the appropriate stage occurs and the process begins again.

Practical Application

Computer modeling is used for a wide range of tasks, such as:

• analysis of the distribution of pollutants in the atmosphere;
• designing noise barriers to combat noise pollution;
• design

Currently, the concept of “system” in science is not fully defined. Scientists have begun to study complex systems (CS).
In numerous literature on systems analysis and systems engineering, the following basic properties of complex systems are noted:

Property 1. Integrity and articulation.

A complex system is considered as an integral set of elements, characterized by the presence of a large number of interconnected and interacting elements.
The researcher has the subjective possibility of dividing the system into subsystems, the functioning goals of which are subordinated to the general goal of the functioning of the entire system (system focus). Purposefulness is interpreted as the ability of a system to carry out behavior (choice of behavior) in pursuit of achieving a specific goal under conditions of uncertainty and the influence of random factors.

Property 2. Connections.

The presence of significant stable connections (relationships) between elements and/or their properties, exceeding in power (strength) the connections (relationships) of these elements with elements not included in this system(external environment).
By “connections” we mean a certain virtual channel through which matter, energy, and information are exchanged between elements and the external environment.

Property 3. Organization.

The property is characterized by the presence of a certain organization - the formation of significant connections of elements, the ordered distribution of connections and elements in time and space. When connections are formed, a certain structure of the system is formed, and the properties of the elements are transformed into functions (actions, behavior).

When studying complex systems, it is usually noted:

• the complexity of the function performed by the system and aimed at achieving a given operating goal;
• presence of control, branched information network and intensive flows of information;
• the presence of interaction with the external environment and functioning under conditions of uncertainty and the influence of random factors of various natures.

Property 4. Integrative qualities.

The existence of integrative qualities (properties), i.e. such qualities that are inherent in the system as a whole, but not characteristic of any of its elements separately. The presence of integrative qualities shows that the properties of the system, although they depend on the properties of the elements, are not completely determined by them.
Examples of SS in the economic sphere are numerous: organizational - production system, enterprise; socially – economic system, for example region; etc.
The methodology for SS research is system analysis. One of the most important tools for applied systems analysis is computer modeling.
Simulation modeling is the most effective and universal version of computer modeling in the field of research and control of complex systems.

Model is an abstract description of a system (object, process, problem, concept) in some form that is different from the form of their real existence.

Modeling is one of the main methods of cognition, is a form of reflection of reality and consists in clarifying or reproducing certain properties of real objects, objects and phenomena with the help of other objects, processes, phenomena, or with the help of an abstract description in the form of an image, plan, map, a set of equations, algorithms and programs.

During the modeling process there is always original(object) and model, which reproduces (models, describes, imitates) some features of an object.

Modeling is based on the presence of a variety of natural and artificial systems, differing both in purpose and physical embodiment, of similarity or similarity of certain properties: geometric, structural, functional, behavioral. This resemblance may be complete (isomorphism) and partial (homomorphism).

The study of modern SS suggests various model classes. Development information technology can be interpreted as the possibility of implementing models various types within information systems for various purposes, For example, information systems, pattern recognition systems, systems artificial intelligence,decision support systems. These systems are based on models various types: semantic, logical, mathematical, etc.

Let's give a general classification of main types of modeling:

• conceptual modeling– representation of the system using special signs, symbols, operations on them, or using natural or artificial languages;
• physical modeling– the modeled object or process is reproduced based on the similarity relationship resulting from similarity physical processes and phenomena;
• structural-functional modeling– models are diagrams (graphs, block diagrams), graphs, diagrams, tables, drawings with special rules for their combination and transformation;
• mathematical (logical-mathematical) modeling– the construction of the model is carried out using mathematics and logic;
• simulation (software) modeling– in this case, the logical-mathematical model of the system under study is an algorithm for the functioning of the system, implemented in software on a computer.

These types of modeling can be used independently or simultaneously, in some combination (for example, almost all of the listed types of modeling or individual techniques are used in simulation modeling). For example, simulation modeling includes conceptual (in the early stages of the formation of a simulation model) and logical-mathematical (including artificial intelligence methods) modeling to describe individual subsystems of the model, as well as in procedures for processing and analyzing the results of a computational experiment and decision making. The technology for conducting and planning a computational experiment with appropriate mathematical methods was introduced into simulation from physical (experimental field or laboratory) modeling. Finally, structural-functional modeling is used both to create a stratified description of multi-model complexes and to form various diagrammatic representations when creating simulation models.

The concept of computer modeling is interpreted more broadly than the traditional concept of “computer modeling”. Let's bring him.

Computer simulation is a method for solving problems of analysis or synthesis of a complex system based on the use of its computer model.

Computer simulation can be thought of as:

• mathematical modeling;
• simulation modeling;
• stochastic modeling.

Under the term “computer model” understand a conventional image of an object or some system of objects (or processes), described using equations, inequalities, logical relationships, interconnected computer tables, graphs, charts, graphs, drawings, animation fragments, hypertexts, etc. and displaying the structure and relationships between the elements of the object. Computer models described using equations, inequalities, logical relationships, interconnected computer tables, graphs, charts, graphs will be called mathematical. Computer models described using interconnected computer tables, graphs, diagrams, graphs, drawings, animation fragments, hypertexts, etc. and displaying the structure and relationships between the elements of the object, we will call structural and functional;

Computer models (a separate program, a set of programs, a software package), allowing, using a sequence of calculations and graphical display of the results of its work, to reproduce (simulate) the processes of functioning of an object (system of objects) subject to the influence of various, usually random, factors on the object, we'll call imitation.

The essence of computer modeling consists in obtaining quantitative and qualitative results on the existing model. Qualitative results analysis reveals previously unknown properties of a complex system: its structure, dynamics of development, stability, integrity, etc. Quantitative findings mainly have the nature of an analysis of an existing system or a forecast of future values ​​of some variables. The ability to obtain not only qualitative, but also quantitative results is a significant difference between simulation modeling and structural-functional modeling. Simulation modeling has a number of specific features.

The methodology of computer modeling is system analysis(direction of cybernetics, general systems theory), in which the dominant role is given to systems analysts. In contrast to mathematical modeling on a computer, where the methodological basis is: operations research, the theory of mathematical models, decision theory, game theory, etc.

The central procedure of system analysis is the construction of a generalized model that reflects all factors and relationships real system . The subject of computer modeling can be any complex system, any object or process. The categories of goals can be very different. The computer model must reflect all the properties, main factors and relationships of a real complex system, criteria, and limitations.

Computer simulation offers a set of methodological approaches and technological tools used to prepare and make decisions in various areas of research.

The choice of a modeling method to solve a given problem or study a system is an urgent task that a systems analyst must be able to cope with.

For this purpose, we will clarify the place of simulation models and their specificity among models of other classes. In addition, let us clarify some concepts and definitions that a systems analyst deals with during the modeling process. For this purpose, consider procedural and technological scheme for constructing and researching models of complex systems. This diagram (shown on page 6) includes, characteristic of any modeling method, next steps definitions:

1. Systems (subject, problem area);
2. Modeling object;
3. Purpose of models;
4. Requirements for models;
5. Forms of presentation;
6. Type of model description;
7. The nature of the model implementation;
8. Model research method.

The first three stages characterize the object and purpose of the study and practically determine the next stages of modeling. At the same time great value acquires a correct description of the object and formulation of the modeling goal from subject area research.

Subject (problem) area. Study various systems: mathematical, economic, production, social, queuing systems, computing, information and many others.

The model must be built purposefully. A goal-oriented model is a substitute for reality with the degree of abstraction necessary for the goal. That is, the model, first of all, must reflect those essential properties and those aspects of the modeled object that are determined by the task. At the same time, it is important to correctly identify and formulate the problem, to clearly define the purpose of the research carried out using modeling.

Model requirements. Modeling is associated with solving real problems and it is necessary to be sure that the simulation results reflect the true state of affairs with a sufficient degree of accuracy, i.e. the model is adequate to reality.

A good model must satisfy some generally accepted requirements. This model should be:

• adequate;
• reliable;
• simple and user-friendly;
• purposeful;
• convenient to manage and handle;
• functionally complete in terms of the ability to solve main problems;
• adaptive, allowing you to easily move to other modifications or update data;
• allowing for change (during operation it may become more complex).

Depending on the target orientation of the model, special requirements are specified for it. The most characteristic are: integrity, reflection of information properties, multi-level, multiplicity (multi-model), extensibility, universality, feasibility (the real possibility of constructing the model itself and its research), realizability (for example, on a computer, the possibility of materializing the model in the form of a real system in design tasks ), efficiency (the costs of time, labor, material and other types of resources for building models and conducting experiments are within acceptable limits or justified). The significance or priority of the requirements for the model directly follows from the purpose of the model. For example, in research problems, management problems, planning and description, an important requirement is the adequacy of the model of objective reality. In problems of design and synthesis of unique systems, an important requirement is the feasibility of the model, for example, in a CAD system or a decision support system (DSS).

The purpose of modeling and setting the requirements for the model determine model presentation form.

Any model (before becoming an objectively existing object) must exist in mental form, be constructively developed, translated into symbolic form and materialized. Thus, three forms of model presentation can be distinguished:

• mental(images);
• iconic(structural diagrams, descriptions in the form of oral and written presentation, logical, mathematical, logical-mathematical constructions);
• material(laboratory and operational mock-ups, prototypes).

A special place in modeling is occupied by iconic, in particular logical, mathematical, logical-mathematical models, as well as models recreated based on descriptions compiled by experts. Iconic models are used to model a variety of systems. This direction is associated with the development computing systems. We will limit ourselves to them in further consideration.

The next stage of the procedural scheme is choosing the type of description and
building a model. For iconic forms, such descriptions can be:

• relation and predicate calculus, semantic networks, frames, artificial intelligence methods, etc. - for logical forms.
• algebraic, differential, integral, integral-differential equations, etc. - for mathematical forms.

Nature of implementationthere are iconic models:

• A analytical(for example, system differential equations can be solved by a mathematician on a piece of paper);
• machine(analog or digital);
• physical(automatic).

In each of them, depending on the complexity of the model, the purpose of the modeling, the degree of uncertainty in the characteristics of the model, there may be different methods of conducting research (experiments), i.e., research methods. For example, in analytical research various mathematical methods are used. In physical or full-scale modeling, an experimental research method is used.

Analysis of current and promising methods of machine experimentation allows us to highlight computational, statistical, simulation and self-organizing research methods.

Computational (mathematical) modeling used in research mathematical models and comes down to their machine implementation with different numerical input data. The results of these implementations (calculations) are presented in graphical or tabular forms. For example, a classic scheme is a machine implementation of a mathematical model, presented in the form of a system of differential equations, based on the use of numerical methods, with the help of which the mathematical model is reduced to an algorithmic form, implemented programmatically on a computer, and calculations are carried out to obtain the results.

Imitation modeling is characterized by a high degree of generality, creates the prerequisites for the creation of a unified model, easily adaptable to a wide class of problems, and acts as a means for integrating models of different classes.

Language is a sign system used for the purposes of communication and cognition.

Languages ​​can be divided into natural And artificial.

Natural (ordinary, spoken) languages ​​develop spontaneously and over time. Artificial languages ​​are created by people for special purposes or for certain groups of people (mathematical language, maritime language, programming languages, etc.). Their characteristic feature is the unambiguous definition of their vocabulary, the rules for the formation of expressions and constructions (strictly formalized). In natural languages ​​they are partially formalized. Each language is characterized by: set of signs used;

The rule for the formation of linguistic constructions from these signs;

A set of syntactic, semantic and pragmatic rules for the use of language constructions.

Alphabet is an ordered set of signs used in a language.

In computer science, we are primarily interested in models that can be created and examined using a computer. Using a computer, you can create and explore many objects: texts, graphs, tables, diagrams, etc. Computer technology are leaving an ever greater imprint on the modeling process, so computer modeling can be considered as a special type of information modeling.

In recent years, thanks to the development GUI and graphic packages, computer, structural and functional modeling has received widespread development. The essence of computer simulation is to obtain quantitative and qualitative results of the functioning of the simulated system using the existing model. Qualitative conclusions obtained from the analysis of the model make it possible to discover previously unknown properties of a complex system: its structure, dynamics of development, stability, integrity, etc. Quantitative conclusions are mainly in the nature of a forecast of some future or explanation of past values ​​of parameters characterizing the system.

The subject of computer modeling can be: the economic activity of a company or bank, an industrial enterprise, an information and computer network, process, inflation process, etc.

The goals of computer modeling can be different, but most often it is to obtain data that can be used to prepare and make decisions of an economic, social, organizational or technical nature. The beginning has been made of using the computer even in conceptual modeling, where it is used, for example, in building artificial intelligence systems. Thus, we see that the concept of “computer modeling” is much broader than the traditional concept of “computer modeling” and needs to be clarified, taking into account today's realities.

Let's start with the term "computer model". IN Currently, a computer model is most often understood as:

§ a conventional image of an object or some system of objects (or processes), described using interconnected computer tables, flowcharts, diagrams, graphs, drawings, animation fragments, hypertexts, etc. and displaying the structure and relationships between the elements of the object. We will call computer models of this type structural-functional;

§ a separate program, a set of programs, a software package that allows, using a sequence of calculations and graphical display of their results, to reproduce (simulate) the processes of functioning of an object, a system of objects, subject to the influence of various (usually random) factors on the object. We will further call such models simulation models.

Computer simulation - a method for solving the problem of analysis or synthesis of a complex system based on the use of its computer model.

The essence of computer modeling is to obtain quantitative and qualitative results from the existing model. Qualitative conclusions obtained from the results of the analysis make it possible to discover previously unknown properties of a complex system: its structure, dynamics of development, stability, integrity, etc. Quantitative conclusions are mainly in the nature of a forecast of some future or explanation of past values ​​of variables characterizing the system.

Computer modeling for the generation of new information uses any information that can be updated using a computer.

The process of studying the behavior of any object or system of objects on a computer can be divided into the following stages:

Construction of a content model;

Construction of a mathematical model;

Construction of an information model and algorithm;

Coding the algorithm in a programming language;

Computer experiment.

Security questions

1. What is a model?

2. What are models used for?

3. What is modeling?

4. How are models classified?

5. What are the stages in the process of creating a model?

6. What types of modeling are there?

7. What models characterize information modeling?

8. What is formalization?

9. What features should a sign have?

10.What is the purpose of computer modeling?

11.What is meant by a computer model?

12.What are the main functions and stages of computer modeling?

Computer model(English) computer model), or numerical model(English) computational model) - computer program, running on a separate computer, supercomputer or many interacting computers (computing nodes), implementing a representation of an object, system or concept in a form different from the real one, but close to an algorithmic description, including a set of data characterizing the properties of the system and the dynamics of their change over time .

About computer modeling

Computer models have become a common tool for mathematical modeling and are used in physics, astrophysics, mechanics, chemistry, biology, economics, sociology, meteorology, other sciences and applied problems in various fields of radio electronics, mechanical engineering, automotive industry, etc. Computer models are used to obtain new knowledge about the modeled object or to approximate the behavior of systems that are too complex for analytical study.

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 carry out the so-called. computational experiments, in cases where real experiments are difficult due to financial or physical obstacles or may give unpredictable results. The logic and formalization of computer models makes it possible to determine 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.

The construction of a computer model is based on abstraction from the specific nature of the phenomena or the original object being studied and consists of two stages - first the creation of a qualitative and then a quantitative model. The more significant properties are identified and transferred to the computer model, the closer it will be to the real model, the greater the capabilities the system using this model will be able to have. 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.

There are analytical and simulation 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(s) that reproduces the functioning of the system under study by sequentially performing a large number of elementary operations.

Advantages of computer modeling

Computer modeling makes it possible to:

• expand the range of research objects - it becomes possible to study non-repeating phenomena, phenomena of the past and future, objects that are not reproduced in real conditions;
• visualize objects of any nature, including abstract ones;
• explore phenomena and processes in the dynamics of their deployment;
• control time (speed up, slow down, etc.);
• perform repeated tests of the model, each time returning it to its original state;
• obtain various characteristics of an object in numerical or graphical form;
• find the optimal design of an object without making trial copies;
• conduct experiments without risk of negative consequences for human health or the environment.

Main stages of computer modeling

During the process of conducting an experiment, it may become clear that you need:

• adjust the research plan;
• choose a different method for solving the problem;
• improve the algorithm for obtaining results;
• clarify the information model;
• make changes to the problem statement.

In this case, a return to the appropriate stage occurs and the process begins again.

Practical Application

Computer modeling is used for a wide range of tasks, such as:

• analysis of the distribution of pollutants in the atmosphere;
• designing noise barriers to combat noise pollution;
• design of vehicles;
• flight simulators for pilot training;
• emulation of the operation of other electronic devices;
• study of the behavior of buildings, structures and parts under mechanical load;
• predicting the strength of structures and their destruction mechanisms;
• design production processes, for example chemical;
• strategic management of the organization;
• study of the behavior of hydraulic systems: oil pipelines, water supply;
• modeling of robots and automatic manipulators;
• modeling scenarios for urban development;
• modeling of transport systems;
• finite element modeling of crash tests;

Different areas of application of computer models have different requirements for the reliability of the results obtained with their help. Modeling of buildings and aircraft parts requires high precision and confidence, while models of the evolution of cities and socio-economic systems are used to obtain approximate or qualitative results.

Computer simulation algorithms

See also

Write a review about the article "Computer Modeling"

Links

An excerpt characterizing Computer Modeling

On March 3, in all the rooms of the English Club there was a groan of talking voices and, like bees on spring migration, scurried back and forth, sat, stood, converged and dispersed, in uniforms, tailcoats and some others in powder and caftans, members and guests of the club . Powdered, stockinged and booted footmen in livery stood at every door and strained to catch every movement of the guests and members of the club in order to offer their services. Most of those present were old, respectable people with wide, self-confident faces, thick fingers, firm movements and voices. This kind of guests and members sat in well-known, familiar places and met in well-known, familiar circles. A small part of those present consisted of random guests - mainly young people, among whom were Denisov, Rostov and Dolokhov, who was again a Semyonov officer. On the faces of the youth, especially the military, there was an expression of that feeling of contemptuous respect for the elderly, which seems to say to the old generation: we are ready to respect and honor you, but remember that after all, the future belongs to us.
Nesvitsky was there, like an old member of the club. Pierre, who, at the orders of his wife, had let his hair grow, had taken off his glasses and was dressed fashionably, but with a sad and despondent look, walked through the halls. He, as everywhere else, was surrounded by an atmosphere of people who worshiped his wealth, and he treated them with the habit of kingship and absent-minded contempt.
According to his years, he should have been with the young; according to his wealth and connections, he was a member of the circles of old, respectable guests, and therefore he moved from one circle to another.
The most important old men formed the center of the circles, to which even strangers respectfully approached to listen. famous people. Large circles were formed around Count Rostopchin, Valuev and Naryshkin. Rostopchin talked about how the Russians were crushed by the fleeing Austrians and had to make their way through the fugitives with a bayonet.
Valuev confidentially said that Uvarov was sent from St. Petersburg in order to find out the opinion of Muscovites about Austerlitz.
In the third circle, Naryshkin spoke about a meeting of the Austrian military council, in which Suvorov crowed the rooster in response to the stupidity of the Austrian generals. Shinshin, who was standing right there, wanted to joke, saying that Kutuzov, apparently, could not learn even this simple art of cockcrow from Suvorov; but the old men looked sternly at the joker, letting him feel that here and today it was so indecent to talk about Kutuzov.
Count Ilya Andreich Rostov, anxiously, hurriedly walked in his soft boots from the dining room to the living room, hastily and in exactly the same way greeting important and unimportant persons whom he knew all, and occasionally looking for his slender young son with his eyes, joyfully resting his gaze on him and winked at him. Young Rostov stood at the window with Dolokhov, whom he had recently met and whose acquaintance he valued. The old count approached them and shook Dolokhov's hand.
- You are welcome to me, you know my fellow... together there, together they were heroes... A! Vasily Ignatich... is very old,” he turned to a passing old man, but before he could finish his greeting, everything began to stir, and a footman who came running, with a frightened face, reported: “You’re here!”