Computer modeling capabilities. Computer modelling

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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 sign logical expressions) reflecting 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 consider the process computer modeling in details.

2.2. Introduction to Computer Modeling

Computer modeling is one of the effective methods studying complex systems. Computer models easier and more convenient to research 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 being studied (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 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 are studied real object in the form of algebraic, differential and other equations, as well as providing for 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:

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 of an 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 in different 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 you to short time and without significant material costs, carry out the study of a large number of options for the 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 ones are the 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 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

Simulation in spreadsheets covers a very wide class of problems in different subject areas. Spreadsheets – universal tool, which 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. There are also additional tasks: 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 a 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.

The computer dashboard 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, and allows, using mathematical methods, to clarify and 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 full-scale experiment is dangerous for human life and health, a computational experiment is the only possible one (thermonuclear fusion, development outer space, 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 a 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. Tutorial. – Tomsk, School University, 2008. – 208 p.

2. A. V. Mogilev, N. I. Pak, E. K. Henner. Computer science. Tutorial. – M.: Center “Academy”, 2000. – 816 p.

3. D. A. Poselov. Computer science. 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

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Introduction

2.2. Task 2. Modeling autowave processes

Conclusion

Bibliography

Introduction

Simulation in scientific research began to be used in ancient times and gradually captured more and more new areas of scientific knowledge. Every physicist has a desire to “see the invisible,” that is, to look into the flow physical phenomenon and see the mechanism, even when it is hidden from direct perception. And here they came to the rescue Computer techologies, namely computer modeling, which allows you to create and see “virtual” experiments and models.

Computer modeling methods appeared in physics in the late 50s and early 60s. The main ones are the dynamic method and the Monte Carlo method. The development of machine modeling methods had a strong impact on physics, since for the first time it became possible to theoretically study systems with sufficient complex interaction particles with each other. Today, these methods are successfully used in solid state physics and in the physics of phase transitions. Using these methods, the properties of liquids, dense plasma, surface phenomena, the passage of radiation through matter and other processes are studied. All this has led to the fact that it is currently customary to divide physics into experimental, theoretical, and computational. Computational physics occupies an intermediate position between experimental and theoretical: the object of its study, on the one hand, is not a real experiment, on the other hand, it is not entirely a theory, since the models of computational physics contain few approximations and are very realistic. Therefore, in this regard, they often talk about a virtual or computer experiment. Until the end of the 80s, machine modeling methods were not available to many; computer experiments were quite expensive, they required a lot of computer time; in addition, the speed of computers and their RAM were relatively small, which greatly limited them graphic capabilities full dialogue between the machine and the user. But the computer boom that has occurred over the past decade has given rise to a series of cheap and affordable computers. The sharp increase in their performance has made the use of machine modeling methods relevant in education, not only for training future specialists in these issues, but also for creating educational physical models that could be used by any users with any computer support.

Relevance of course work. In connection with the massive equipment of schools with computers under the all-Russian computerization program, interest in the use of computers in subject teaching has deepened. Computer like technical means opens up great opportunities for improving the educational process. However, the use of computers in teaching subjects, in particular physics, is not widespread and is limited. On the one hand, this is due to insufficient methodological development software and training programs. The identification of this issue is observed in the dissertation research of A.M. Korotkova, L.Yu. Kravchenko, E.A. Loktyushina, N.A. Gomulina, A.S. Kameneva, Sh.D. Makhmudova. On the other hand, the computer programs in physics offered by developers are mostly closed to the user: they include a ready-made bank of problems, tests, theory and demonstrations, which are not always combined with the teacher’s teaching methods and are often not linked to the educational process either organizationally or methodically. Programs that make it possible to achieve openness for the user usually do not support the solution of physical problems or are quite cumbersome to learn; they require knowledge of programming languages - Pascal, C++, Delphi or numerical methods - Mathcad, Excel. Therefore, the search for general approaches and methods that increase the effectiveness of teaching physics using a computer remains relevant. In particular, the problem of creating an environment in which traditional and computer methods training. One of the effective methods of teaching solving physical problems is the computer modeling method, which integrates didactic opportunities in teaching problem solving and is a means of developing the mental and creative abilities of students. And the introduction of new educational technologies V educational process allows along with traditional methods apply modeling to solve problems.

The purpose of the course work is to study and research the features of computer modeling in the field of physics.

Based on the goal, the following objectives of the course work were set: to study the basic concepts of computer modeling; systematize material on computer modeling in the field of physics; consider computer modeling using the example of solving specific problems.

The structure of the course work. Course work consists of contents, introduction, two chapters, conclusion and bibliography.

1. Theoretical part. Computer modelling

1.1 Concept of computer modeling

With the development of computer technology, the role of computer modeling in solving applied and scientific tasks. To conduct computer experiments, a suitable mathematical model is created and appropriate development tools are selected software. The choice of programming language has a huge impact on the implementation of the resulting model.

Traditionally, computer modeling meant only simulation modeling. It can be seen, however, that in other types of modeling a computer can be extremely useful, with the exception of physical modeling, where a computer can also be used, but rather for the purpose of managing the modeling process. For example, in mathematical modeling, performing one of the main stages - constructing mathematical models based on experimental data - is currently simply unthinkable without a computer. IN last years, thanks to the development of the graphical interface and graphic packages, computer, structural and functional modeling has become widespread. 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".

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;

§ 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 modeling is 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 lies in the acquisition of 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.

Basic computer functions for modeling:

§ to perform the role aid for solving problems solved by conventional computing means, algorithms, technologies;

§ act as a means of setting and solving new problems that cannot be solved by traditional means, algorithms, and technologies;

§ act as a means of constructing computer teaching and modeling environments;

§ act as a modeling tool to obtain new knowledge;

§ perform the role of “training” new models (self-learning models).

One type of computer modeling is a computational experiment.

A computer model is a model of a real process or phenomenon, implemented by computer means. If the state of the system changes over time, then the models are called dynamic, otherwise - static.

Processes in a system can occur differently depending on the conditions in which the system is located. Observe behavior real system under different conditions it can be difficult and sometimes impossible. In such cases, having built a model, you can repeatedly return to the initial state and observe its behavior. This method of studying systems is called simulation modeling.

An example of simulation modeling could be calculating the number =3.1415922653... using the Monte Carlo method. This method allows you to find the areas and volumes of figures (bodies) that are difficult to calculate by other methods. Suppose you want to determine the area of a circle. Let's draw a square around it (the area of which, as is known, is equal to the square of its side) and randomly throw points into the square, checking each time whether the point falls into the circle or not. At large number points, the ratio of the area of the circle to the area of the square will tend to the ratio of the number of points falling into the circle to the total number of thrown points.

The theoretical basis of this method was known for a long time, but before the advent of computers this method could not find any widespread application, because modeling random variables manually is a very labor-intensive job. The name of the method comes from the city of Monte Carlo in the Principality of Monaco, famous for its gambling houses, because one of the mechanical devices to obtain random variables is a roulette wheel.

It should be noted that this method calculating the area of a circle will give the correct result only if the points are not just random, but also evenly scattered throughout the square. For modeling uniformly distributed in the range from 0 to 1 random numbers A random number sensor is used - a special computer program. In fact, these numbers are determined by some algorithm and for this reason they are not completely random. The numbers obtained in this way are often called pseudorandom. The question of the quality of random number sensors is quite complex, but for solving not too complex problems, the capabilities of the sensors built into most programming systems and spreadsheets are usually sufficient.

Note that having a sensor of uniformly distributed random numbers that generates numbers r from the interval into the array xxii[i] and calculates the speeds of the elements at time t+Дt:

зi(t+Дt)=зi(t)+ v2[(оi+1-2оi +оi-1)/h2]Дt.

writing them to the array o[i].

5. The loop goes through all the elements and calculates their offsets using the formula:

oi(t+Дt)=оi(t)+ зi(t+Дt)Дt.

6. In the loop, they go through all the elements, erase their previous images and draw new ones.

7. Return to operation 2. If the cycle by t has ended, exit the cycle.

4. Computer program. The proposed program simulates the passage and reflection of an impulse from the “interface between two media.”

program PROGRAMMA1;

uses crt, graph;

const n=200; h=1; dt=0.05;

var i, j, DriverVar,

ModeVar, ErrorCode: integer;

eta,xi,xxii: array of real;

Procedure Graph_Init;

begin (- Graphics initialization -)

DriverVar:=Detect;

InitGraph(DriverVar,ModeVar,"c:\bp\bgi");

ErrorCode:=GraphResult;

if ErrorCode<>grOK then Halt(1);

Procedure Calculation; (Offset calculation)

begin for i:=2 to N-1 do

if i

eta[i]:=eta[i]+vv*(xi-2*xi[i]+xi)/(h*h)*dt;

for i:=2 to N-1 do xi[i]:=xi[i]+eta[i]*dt;

xi[N]:=0; (End secured)

( xi[N]:=xi;)( loose)

begin (- Output to screen -)

setcolor(black);

line(i*3-3,240-round(xxii*50),i*3,240-round(xxii[i]*50));

setcolor(white);

line(i*3-3,240-round(xi*50),i*3,240-round(xi[i]*50));

BEGIN (- Main program -)

if t<6.28 then xi:=2*sin(t) else xi:=0;

Raschet; For i:=1 to N do Draw;

until KeyPressed; CloseGraph;

The computer model discussed above makes it possible to perform a series of numerical experiments and study the following phenomena: 1) propagation and reflection of a wave (single pulse, train) from the fixed and unfixed end of the elastic medium; 2) interference of waves (single pulses, trains), resulting from the reflection of an incident wave or the radiation of two coherent waves; 3) reflection and passage of a wave (single pulse, train) across the interface between two media; 4) study of the dependence of wavelength on frequency and propagation speed; 5) observation of a change in the phase of the reflected wave by p when reflected from a medium in which the wave speed is lower.

2.2 Task 2. Modeling of autowave processes

1. Problem: There is a two-dimensional active medium consisting of elements, each of which can be in three different states: rest, excitation and refractoriness. In the absence of external influence, the element is at rest. As a result of the impact, the element goes into an excited state, acquiring the ability to excite neighboring elements. Some time after excitation, the element switches to a state of refractoriness, in which it cannot be excited. Then the element itself returns to its original state of rest, that is, it again acquires the ability to pass into an excited state. It is necessary to simulate the processes occurring in a two-dimensional active medium with different parameters of the medium and the initial distribution of excited elements.

2. Theory. Let's consider the generalized Wiener-Rosenbluth model. Let's mentally divide the computer screen into elements determined by the indices i, j and forming a two-dimensional network. Let the state of each element be described by the phase yi,j (t), and the activator concentration uij (t), where t is a discrete point in time.

If the element is at rest, then we will assume that yi,j (t) = 0. If, due to the proximity of excited elements, the concentration of the activator uij (t) reaches the threshold value h, then the element is excited and goes into state 1. Then, at the next step, it switches to state 2, then to state 3, etc., while remaining excited. Having reached the r state, the element enters the refractory state. After (s - r) steps after excitation, the element returns to its resting state.

We assume that upon transition from state s to rest state 0, the activator concentration becomes equal to 0. If there is a neighboring element in an excited state, it increases by 1. If p nearest neighbors are excited, then at the corresponding step the activator concentration is added to the previous value number of excited neighbors:

uij (t + Дt) = uij (t) + p.

You can limit yourself to taking into account the nearest eight neighboring elements.

3. Algorithm. To model autowave processes in an active medium, it is necessary to create a time cycle in which the phases of the elements of the medium at subsequent times and the concentration of the activator are calculated, the previous distribution of excited elements is erased and a new one is constructed. The model algorithm is presented below.

1. Set the number of elements of the active medium, its parameters s, r, h, and the initial distribution of excited elements.

2. Start of the cycle at t. They give a time increment: the variable t is assigned the value t + Дt.

3. All elements of the active medium are sorted out, determining their phases yi,j (t + Дt) and the activator concentration ui,j (t + Дt) at the moment t + Дt.

4. Clear the screen and build excited elements of the active medium.

5. Return to operation 2. If the cycle by t has ended, exit the cycle.

4. Computer program. Below is a program that simulates the active medium and the processes occurring in it. The program specifies the initial phase values yi,j (t + Дt) of all elements of the active medium, and also has a time cycle in which the values of yi,j (t + Дt) are calculated at the next moment t + Дt and the results are displayed graphically on screen. The parameters of the environment are r = 6, s = 13, h = 5, that is, each element, except for the rest state, can be in 6 excited states and 7 refractory states. The threshold value of the activator concentration is 5. The program builds a one-arm wave, an oscillator and an obstacle.

Program PROGRAMMA2;

uses dos, crt, graph;

Const N=110; M=90; s=13; r=6; h=5;

Var y, yy, u: array of integer;

ii, jj, j, k, Gd, Gm: integer; i:Longint;

Gd:= Detect; InitGraph(Gd, Gm, "c:\bp\bgi");

If GraphResult<>grOk then Halt(1);

setcolor(8); setbkcolor(15);

(* y:=1; (Single wave) *)

For j:=1 to 45 do (One-armed wave)

For i:=1 to 13 do y:=i;

(* For j:=1 to M do (Two-armed wave)

For i:=1 to 13 do begin y:=i;

If j>40 then y:=14-i; end; *)

If k=round(k/20)*20 then y:=1; (Oscillator 1)

(* If k=round(k/30)*30 then y:=1; (Oscillator 2) *)

For i:=2 to N-1 do For j:=2 to M-1 do begin

If (y>0) and (y

If y=s then begin yy:=0; u:=0; end;

If y<>0 then goto met;

For ii:=i-1 to i+1 do For jj:=j-1 to j+1 do begin

If (y>0) and (y<=r) then u:=u+1;

If u>=h then yy:=1; end;

met:end; Delay(2000); (Delay)

For i:=21 to 70 do begin

yy:=0; yy:=0; (Let)

circle(6*i-10,500-6*60,3); circle(6*i-10,500-6*61,3); end;

For i:=1 to N do For j:=1 to M do

begin y:=yy; setcolor(12);

If (y>=1) and (y<=r) then circle(6*i-10,500-6*j,3);

If (y>6) and (y<=s) then circle(6*i-10,500-6*j,2);

until KeyPressed;

Conclusion

In almost all natural and social sciences, the construction and use of models is a powerful research tool. Real objects and processes can be so multifaceted and complex that the best way to study them is to build a model that reflects only some part of reality and is therefore many times simpler than this reality. The subject of research and development of computer science is the methodology of information modeling associated with the use of computer equipment and technologies. In this sense, they talk about computer modeling. The interdisciplinary significance of computer science is largely manifested through the introduction of computer modeling in various scientific and applied fields: physics and technology, biology and medicine, economics, management and many others.

Currently, with the development of computer technology and the rise in price of the components of experimental installations, the role of computer modeling in physics is significantly increasing. There is no doubt about the need for a visual demonstration of the dependencies studied during the learning process for their better understanding and memorization. It is also relevant to teach students in educational institutions the basics of computer literacy and computer modeling. At the present stage, computer modeling in the field of physics is a very popular form of education.

Bibliography

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2. Bulavin L.A., Vygornitsky N.V., Lebovka N.I. Computer modeling of physical systems. - Dolgoprudny: Publishing House "Intelligence", 2011. - 352 p.

3. Gould H., Tobochnik Y. Computer modeling in physics: In 2 parts. Part one. - M.: Mir, 2003. - 400 p.

4. Desnenko S.I., Desnenko M.A. Modeling in physics: Educational

Methodological manual: In 2 hours - Chita: ZabSPU Publishing House, 2003. - Part I. - 53 p.

5. Kuznetsova Yu.V. Special course “Computer modeling in physics” / Yu.V. Kuznetsova // Physics in school. - 2008. - No. 6. - 41 s.

6. Lychkina N.N. Modern trends in simulation modeling. - University Bulletin, series Management Information Systems No. 2 - M., State University of Management, 2000. - 136 p.

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Features of computer modeling

The improvement of computing technology and the widespread use of personal computers have opened up enormous prospects for modeling for the study of processes and phenomena in the surrounding world, including human society.

Computer modeling is, to a certain extent, the same as the modeling described above, but implemented using computer technology.

For computer modeling, it is important to have certain software.

At the same time, the software by means of which computer modeling can be carried out can be both quite universal (for example, ordinary text and graphic processors) and very specialized, intended only for a certain type of modeling.

Very often computers are used for mathematical modeling. Here their role is invaluable in performing numerical operations, while the analysis of the problem usually falls on the shoulders of a person.

Typically, in computer modeling, different types of modeling complement each other. So, if the mathematical formula is very complex, which does not give a clear idea of the processes it describes, then graphical and simulation models come to the rescue. Computer visualization can be much cheaper than actually creating natural models.

With the advent of powerful computers, graphic modeling based on engineering systems for creating drawings, diagrams, and graphs has spread.

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

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 performing a large number of elementary operations.

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.

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 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

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.

Computer modeling is widely used in various branches of science and technology, gradually replacing real experiments and experiences. It has become so firmly established in our lives that it is already quite difficult to imagine a situation when we will have to abandon this method of studying the real world. This phenomenon is explained quite easily: with the help of this process, you can achieve significant results in the shortest possible time, allowing you to penetrate into that area of reality that is not achievable for humans.

Computer science allows you to create a model on a computer that, with some assumption, has the properties of a real object or process, and the research is carried out precisely on this created model. To conduct research, you need to accurately understand why it is being carried out, what its purpose is, what properties and aspects of the object being studied interest you. Only in this case can you be sure of a positive result.

Like any other process, computer modeling is built according to certain principles, among which the following can be distinguished:

· the principle of information sufficiency. If there is insufficient information about the real process or object, it will most likely not be possible to conduct research using this method;

· the principle of feasibility. The created model should allow achieving the goals set for the researcher;

· the principle of multiplicity of models, which is based on the fact that in order to study all the properties of a real object it is necessary to develop several models, since it is not possible to combine all real properties in one;

· principle of aggregation. In this case, a complex object is represented in the form of separate blocks that can be rearranged in a certain way;

· the principle of paramerization, which allows the parameters of a certain subsystem to be replaced with numerical values, which, while reducing the volume and duration of modeling, also reduces the adequacy of the resulting model. Therefore, the application of this principle must be fully justified.

Computer modeling must be performed in a certain, strictly defined sequence. At the first stage, the goal is determined, after which development is carried out. Then the model is formalized, allowing for its software implementation. After this, you can begin to plan model experiments and implement the previously compiled ones. After all the previous points have been completed, it will be possible to analyze and interpret the results obtained.

Recently, computer modeling of physical processes has been carried out using various You can find a large number of works performed in Matlab. Such studies make it possible to study all sorts of physical processes that humans cannot observe in reality.

Computer modeling is widely used in industry. With its help, new products are developed, new machines are designed, their operating conditions are set and virtual tests are carried out. If the compiled model has a sufficient degree of adequacy, it can be argued that the results of real tests will be similar to virtual ones. In addition to studying the properties of a particular system, you can use a computer to design the appearance of the finished product and set its parameters. This minimizes the amount of defects that may arise as a result of inaccurate engineering calculations.

Computer modeling capabilities. Computer modelling

2.2. Introduction to Computer Modeling

2.3. Building a computer model

2.4. Computational experiment

2.5. Simulation in various environments

2.5.1. Simulation in a programming environment

2.5.2. Modeling in Spreadsheets

2.5.3. Modeling in a DBMS environment

2.6. Using a computer model

2.7. Conclusion

3. List of references used

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

2. A. V. Mogilev, N. I. Pak, E. K. Henner. Computer science. Tutorial. – M.: Center “Academy”, 2000. – 816 p.

3. D. A. Poselov. Computer science. 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

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