| Lesson planning for the school year | Main stages of modeling

Lesson 2
Main stages of modeling

By studying this topic, you will learn:

What is modeling;
- what can serve as a prototype for modeling;
- what is the place of modeling in human activity;
- what are the main stages of modeling;
- what is a computer model;
What is a computer experiment.

computer experiment

To give life to new design developments, to introduce new technical solutions into production or to test new ideas, an experiment is needed. An experiment is an experiment that is performed with an object or model. It consists in performing some actions and determining how the experimental sample reacts to these actions.

At school, you conduct experiments in the lessons of biology, chemistry, physics, geography.

Experiments are carried out when testing new product samples at enterprises. Usually, a specially created setup is used for this purpose, which makes it possible to conduct an experiment in laboratory conditions, or the real product itself is subjected to all kinds of tests (a full-scale experiment). To study, for example, the performance properties of a unit or assembly, it is placed in a thermostat, frozen in special chambers, tested on vibration stands, dropped, etc. It is good if it is a new watch or a vacuum cleaner - the loss during destruction is not great. What if it's a plane or a rocket?

Laboratory and full-scale experiments require large material costs and time, but their significance, nevertheless, is very great.

With the development of computer technology, a new unique method of research has appeared - a computer experiment. In many cases, computer simulation studies have come to help, and sometimes even to replace, experimental samples and test benches. The stage of conducting a computer experiment includes two stages: drawing up an experiment plan and conducting a study.

Experiment plan

The experiment plan should clearly reflect the sequence of work with the model. The first step in such a plan is always to test the model.

Testing is the process of checking the correctness of the constructed model.

Test - a set of initial data that allows you to determine the correctness of the construction of the model.

To be sure of the correctness of the obtained modeling results, it is necessary: ♦ to check the developed algorithm for building the model; ♦ make sure that the constructed model correctly reflects the properties of the original, which were taken into account in the simulation.

To check the correctness of the model construction algorithm, a test set of initial data is used, for which the final result is known in advance or predetermined in other ways.

For example, if you use calculation formulas in modeling, then you need to select several options for the initial data and calculate them “manually”. This test tasks. When the model is built, you test with the same inputs and compare the results of the simulation with the conclusions obtained by calculation. If the results match, then the algorithm is developed correctly, if not, it is necessary to look for and eliminate the cause of their discrepancy. Test data may not reflect the real situation at all and may not carry semantic content. However, the results obtained during the testing process may prompt you to think about changing the original informational or sign model, primarily in that part of it where the semantic content is laid down.

To make sure that the constructed model reflects the properties of the original, which were taken into account in the simulation, it is necessary to select a test example with real source data.

Conducting research

After testing, when you have confidence in the correctness of the constructed model, you can proceed directly to the study.

The plan should include an experiment or series of experiments that meet the objectives of the simulation. Each experiment must be accompanied by an understanding of the results, which serves as the basis for analyzing the results of modeling and making decisions.

The scheme for preparing and conducting a computer experiment is shown in Figure 11.7.

Rice. 11.7. Scheme of a computer experiment

Analysis of simulation results

The ultimate goal of modeling is to make a decision, which should be developed on the basis of a comprehensive analysis of the simulation results. This stage is decisive - either you continue the study, or finish. Figure 11.2 shows that the results analysis phase cannot exist autonomously. The conclusions obtained often contribute to an additional series of experiments, and sometimes to a change in the problem.

The results of testing and experiments serve as the basis for developing a solution. If the results do not correspond to the goals of the task, it means that mistakes were made at the previous stages. This may be either an incorrect statement of the problem, or an overly simplified construction of an information model, or an unsuccessful choice of a modeling method or environment, or a violation of technological methods when building a model. If such errors are identified, then the model needs to be corrected, that is, a return to one of the previous stages. The process is repeated until the results of the experiment meet the objectives of the simulation.

The main thing to remember is that the detected error is also the result. As the proverb says, you learn from your mistakes. The great Russian poet A. S. Pushkin also wrote about this:

Oh, how many wonderful discoveries we have
Prepare enlightenment spirit
And experience, the son of difficult mistakes,
And genius, paradoxes friend,
And chance, god is the inventor...

Control questions and tasks

1. What are the two main types of modeling problem statement.

2. In the well-known "Problem Book" by G. Oster, there is the following problem:

The evil witch, working tirelessly, turns 30 princesses into caterpillars a day. How many days will it take her to turn 810 princesses into caterpillars? How many princesses a day would have to be turned into caterpillars to get the job done in 15 days?
Which question can be attributed to the type of "what will happen if ...", and which - to the type of "how to do so that ..."?

3. List the most well-known goals of modeling.

4. Formalize the playful problem from G. Oster's "Problem Book":

From two booths located at a distance of 27 km from one another, two pugnacious dogs jumped out towards each other at the same time. The first runs at a speed of 4 km / h, and the second - 5 km / h.
How long will the fight start?

5. Name as many characteristics of the "pair of shoes" object as you can. Compose an information model of an object for different purposes:
■ choice of footwear for hiking;
■ selection of a suitable shoe box;
■ purchase of shoe care cream.

6. What characteristics of a teenager are essential for a recommendation on choosing a profession?

7. Why is the computer widely used in simulation?

8. Name the tools of computer modeling known to you.

9. What is a computer experiment? Give an example.

10. What is model testing?

11. What errors are encountered in the modeling process? What should be done when an error is found?

12. What is the analysis of simulation results? What conclusions are usually drawn?

Computer experiment Computer experiment To give life to new design developments, to introduce new technical solutions into production, or to test new ideas, an experiment is needed. In the recent past, such an experiment could be carried out either in laboratory conditions on facilities specially created for it, or in nature, i.e. on a real sample of the product, subjecting it to all sorts of tests. This requires a lot of money and time. Computer simulations came to the rescue. When conducting a computer experiment, the correctness of building models is checked. The behavior of the model is studied for various parameters of the object. Each experiment is accompanied by a comprehension of the results. If the results of a computer experiment contradict the meaning of the problem being solved, then the error must be sought in an incorrectly chosen model or in the algorithm and method for solving it. After identifying and eliminating errors, the computer experiment is repeated. To give life to new design developments, to introduce new technical solutions into production or to test new ideas, an experiment is needed. In the recent past, such an experiment could be carried out either in laboratory conditions on facilities specially created for it, or in nature, i.e. on a real sample of the product, subjecting it to all sorts of tests. This requires a lot of money and time. Computer simulations came to the rescue. When conducting a computer experiment, the correctness of building models is checked. The behavior of the model is studied for various parameters of the object. Each experiment is accompanied by a comprehension of the results. If the results of a computer experiment contradict the meaning of the problem being solved, then the error must be sought in an incorrectly chosen model or in the algorithm and method for solving it. After identifying and eliminating errors, the computer experiment is repeated.

A mathematical model is understood as a system of mathematical correlations of formulas, equations of inequalities, etc., reflecting the essential properties of an object or process. A mathematical model is understood as a system of mathematical correlations of formulas, equations of inequalities, etc., reflecting the essential properties of an object or process.

Modeling problems from different subject areas Modeling problems from different subject areas Economics Economics Economics Astronomy Astronomy Astronomy Physics Physics Physics Ecology Ecology Ecology Biology Biology Biology Geography Geography Geography

The machine-building plant, selling products at contractual prices, received a certain amount of revenue by spending a certain amount of money on production. Determine the ratio of net profit to invested funds. The machine-building plant, selling products at contractual prices, received a certain amount of revenue by spending a certain amount of money on production. Determine the ratio of net profit to invested funds. Statement of the problem Statement of the problem The purpose of modeling is to investigate the process of production and sale of products in order to obtain the greatest net profit. Using economic formulas, find the ratio of net profit to invested funds. The purpose of modeling is to explore the process of production and sale of products in order to obtain the greatest net profit. Using economic formulas, find the ratio of net profit to invested funds.

The main parameters of the simulation object are: revenue, cost, profit, profitability, profit tax. The main parameters of the simulation object are: revenue, cost, profit, profitability, profit tax. Initial data: Initial data: revenue B; revenue B; costs (cost) S. costs (cost) S. We will find other parameters using the main economic dependencies. The value of profit is defined as the difference between revenue and cost P=B-S. We will find other parameters using the main economic dependencies. The value of profit is defined as the difference between revenue and cost P=B-S. Profitability r is calculated by the formula:. Profitability r is calculated by the formula:. The profit corresponding to the marginal level of profitability of 50% is 50% of the production cost S, i.e. S*50/100=S/2, so the profit tax N is defined as follows: S*50/100=S/2, so the profit tax N is defined as follows: if r

Analysis of the results Analysis of the results The resulting model allows, depending on the profitability, to determine the profit tax, automatically recalculate the amount of net profit, and find the ratio of net profit to invested funds. The resulting model allows, depending on the profitability, to determine the profit tax, automatically recalculate the amount of net profit, and find the ratio of net profit to invested funds. The conducted computer experiment shows that the ratio of net profit to invested funds increases with an increase in revenue and decreases with an increase in the cost of production. The conducted computer experiment shows that the ratio of net profit to invested funds increases with an increase in revenue and decreases with an increase in the cost of production.

Task. Task. Determine the speed of the planets in their orbit. To do this, create a computer model solar system. Statement of the problem The purpose of the simulation is to determine the speed of the planets in orbit. Modeling object The solar system, the elements of which are the planets. The internal structure of the planets is not taken into account. We will consider the planets as elements that have the following characteristics: Name; R is the distance from the Sun (in astronomical units; astronomical units is the average distance from the Earth to the Sun); t is the period of revolution around the Sun (in years); V is the speed of movement along the orbit (astro units/year), assuming that the planets move around the Sun in circles at a constant speed.

Analyzing the results Analyzing the results 1. Analyze the calculation results. Can it be argued that the planets that are closer to the Sun have a greater orbital speed? 1. Analyze the calculation results. Can it be argued that the planets that are closer to the Sun have a greater orbital speed? 2. The presented model of the solar system is static. When constructing this model, we neglected changes in the distance from the planets to the Sun during their orbital motion. To know which planet is farther and what are the approximate relationships between distances, this information is quite enough. If we want to determine the distance between the Earth and Mars, then we cannot neglect temporal changes, and here we will have to use a dynamic model. 2. The presented model of the solar system is static. When constructing this model, we neglected changes in the distance from the planets to the Sun during their orbital motion. To know which planet is farther and what are the approximate relationships between distances, this information is quite enough. If we want to determine the distance between the Earth and Mars, then we cannot neglect temporal changes, and here we will have to use a dynamic model.

Computer experiment Enter the initial data into the computer model. (For example: =0.5; =12) Find such a coefficient of friction at which the car will go downhill (at a given angle). Find such an angle at which the car will stand on the mountain (for a given coefficient of friction). What will be the result if the friction force is neglected. Analysis of the results This computer model allows you to conduct a computational experiment, instead of a physical one. By changing the values of the initial data, you can see all the changes occurring in the system. It is interesting to note that in the constructed model, the result does not depend on either the mass of the car or the free fall acceleration.

Task. Task. Imagine that there is only one source left on Earth fresh water Lake Baikal. For how many years will Baikal provide the population of the whole world with water? Imagine that on Earth there will be only one source of fresh water - Lake Baikal. For how many years will Baikal provide the population of the whole world with water?

Model development Model development To build a mathematical model, let's define the initial data. Denote: To build a mathematical model, we define the initial data. Let us denote: V is the volume of Lake Baikal km3; V is the volume of Lake Baikal km3; N - population of the Earth 6 billion people; N - population of the Earth 6 billion people; p - water consumption per day per person (on average) 300 liters. p - water consumption per day per person (on average) 300 liters. Since 1l. = 1 dm3 of water, it is necessary to convert V of lake water from km3 to dm3. V (km3) \u003d V * 109 (m3) \u003d V * 1012 (dm3) Since 1l. = 1 dm3 of water, it is necessary to convert V of lake water from km3 to dm3. V (km3) \u003d V * 109 (m3) \u003d V * 1012 (dm3) The result is the number of years for which the population of the Earth uses the waters of Lake Baikal, denoted by g. So, g=(V*)/(N*p*365) The result is the number of years for which the population of the Earth uses the waters of Lake Baikal, we denote g. So g=(V*)/(N*p*365) This is what the spreadsheet looks like in formula display mode: This is what the spreadsheet looks like in formula display mode:

Task. Task. For the production of the vaccine, it is planned to grow a culture of bacteria at the plant. It is known that if the mass of bacteria is x g, then in a day it will increase by (a-bx)x g, where the coefficients a and b depend on the type of bacteria. The plant will collect m g of bacteria daily for the needs of vaccine production. To draw up a plan, it is important to know how the mass of bacteria changes after 1, 2, 3, ..., 30 days. For the production of a vaccine, it is planned to grow a culture of bacteria at the plant. It is known that if the mass of bacteria is x g, then in a day it will increase by (a-bx)x g, where the coefficients a and b depend on the type of bacteria. The plant will collect m g of bacteria daily for the needs of vaccine production. To draw up a plan, it is important to know how the mass of bacteria changes after 1, 2, 3, ..., 30 days ..

Statement of the problem Statement of the problem The object of modeling is the process of population change depending on time. This process is influenced by many factors: the environment, the state of medical care, the economic situation in the country, the international situation, and much more. Summarizing the demographic data, scientists have derived a function that expresses the dependence of the population on time: The object of modeling is the process of changing the population depending on time. This process is influenced by many factors: the environment, the state of medical care, the economic situation in the country, the international situation, and much more. Summarizing the demographic data, the scientists derived a function that expresses the dependence of the population on time: f(t)=where the coefficients a and b are different for each state, f(t)=where the coefficients a and b are different for each state, e is the base of the natural logarithm. e is the base of the natural logarithm. This formula only approximately reflects reality. To find the values of the coefficients a and b, you can use the statistical handbook. Taking the values of f(t) (population at time t) from the reference book, one can approximately select a and b so that the theoretical values of f(t) calculated by the formula do not differ much from the actual data in the reference book. This formula only approximately reflects reality. To find the values of the coefficients a and b, you can use the statistical handbook. Taking the values of f(t) (population at time t) from the reference book, one can approximately select a and b so that the theoretical values of f(t) calculated by the formula do not differ much from the actual data in the reference book.

Using the computer as a tool learning activities makes it possible to rethink traditional approaches to the study of many issues of natural sciences, to strengthen the experimental activities of students, to bring the learning process closer to the real process of cognition based on modeling technology. The use of a computer as a tool for educational activities makes it possible to rethink traditional approaches to the study of many issues of natural sciences, to strengthen the experimental activities of students, to bring the learning process closer to the real process of cognition based on modeling technology. Solving problems from various areas of human activity on a computer is based not only on students' knowledge of modeling technology, but, of course, on knowledge of this subject area. In this regard, it is more expedient to conduct the proposed lessons on modeling after students have studied the material on a general educational subject, the computer science teacher needs to cooperate with teachers of different educational areas. The experience of conducting binary lessons is known, i.e. lessons conducted by an informatics teacher together with a subject teacher. Solving problems from various areas of human activity on a computer is based not only on students' knowledge of modeling technology, but, of course, on knowledge of this subject area. In this regard, it is more expedient to conduct the proposed modeling lessons after students have studied the material on a general educational subject, the computer science teacher needs to cooperate with teachers from different educational areas. The experience of conducting binary lessons is known, i.e. lessons conducted by an informatics teacher together with a subject teacher.

The modern computer has many uses. Among them, as you know, the capabilities of the computer as a means of automating information processes are of particular importance. But no less significant are its possibilities as tool conducting experimental work and analyzing its results.

Computational experiment has long been known in science. Remember the discovery of the planet Neptune "at the tip of the pen." Often the results of scientific research are considered reliable only if they can be presented in the form mathematical models and confirmed by mathematical calculations. Moreover, this applies not only to physics.

or technical design, but also to sociology, linguistics, marketing - traditionally humanities, far from mathematics.

A computational experiment is a theoretical method of cognition. The development of this method is numerical simulation- a relatively new scientific method that has become widespread due to the advent of computers.

Numerical simulation is widely used both in practice and in scientific research.

Example. Without building mathematical models and performing various calculations on constantly changing data coming from measuring instruments, the operation of automatic production lines, autopilots, tracking stations, and automatic diagnostic systems is impossible. Moreover, to ensure the reliability of systems, calculations must be carried out in real time, and their errors can be millionths of a percent.

Example. A modern astronomer can often be seen not at the eyepiece of a telescope, but in front of a computer display. And not only theorist, but also the observer. Astronomy is an unusual science. She, as a rule, cannot directly experiment with the objects of research. Different kinds radiation (electromagnetic, gravitational, neutrino or cosmic ray fluxes) astronomers only "peep" and "eavesdrop". This means that you need to learn how to extract the maximum information from observations and reproduce them in calculations to test the hypotheses describing these observations. The applications of computers in astronomy, as in other sciences, are extremely diverse. This is both the automation of observations and the processing of their results (astronomers see images not in the eyepiece, but on a monitor connected to special devices). Computers are also needed to work with large catalogs (stars, spectral analyses, chemical compounds, etc.).

Example. Everyone knows the expression "a storm in a teacup". In order to study in detail such a complex hydrodynamic process as a storm, it is necessary to involve complex numerical simulation methods. Therefore, powerful computers are located in large hydrometeorological centers: “a storm is played out” in the computer processor crystal.

Even if you are doing not very complex calculations, but you need to repeat them a million times, then it is better to write a program once, and the computer will repeat it as many times as necessary (the limitation, of course, will be the speed of the computer).

Numerical simulation can be an independent research method when only the values of some indicators are of interest (for example, the cost of production or the integral spectrum of the galaxy), but more often it acts as one of the means of constructing computer models in the broader sense of the term.

Historically, the first work on computer modeling was associated with physics, where a whole class of problems in hydraulics, filtration, heat transfer and heat transfer, mechanics was solved using numerical simulation. solid body etc. Modeling, basically, was a solution of complex nonlinear problems of mathematical physics and, in essence, it was, of course, mathematical modeling. The success of mathematical modeling in physics contributed to its spread to the problems of chemistry, electric power, biology, and the modeling schemes did not differ too much from each other. The complexity of the problems solved on the basis of modeling was limited only by the power of the available computers. This type of modeling is widespread at the present time. Moreover, during the development of numerical simulation, entire libraries of subroutines and functions have been accumulated that facilitate the application and expand the possibilities of simulation. And yet, at present, the concept computer modelling» is usually associated not with fundamental natural science disciplines, but primarily with a system analysis of complex systems from the standpoint of cybernetics (that is, from the standpoint of management, self-management, self-organization). And now computer modeling is widely used in biology, macroeconomics, in the creation of automated control systems, etc.

Example. Recall Piaget's experiment described in the previous paragraph. It, of course, could be carried out not with real objects, but with an animated image on the display screen. But after all, the movement of toys could be filmed on ordinary film and shown on TV. Is it appropriate to call the use of a computer in this case a computer simulation?

Example. The flight model of a body thrown vertically upwards or at an angle to the horizon is, for example, a graph of the height of the body as a function of time. You can build it

a) on a piece of paper point by point;

b) in a graphical editor for the same points;

c) using a business graphics program, for example, in
spreadsheets;

d) writing a program that not only displays
wound flight path, but also allows you to set different
initial data (inclination angle, initial speed
growth).

Why do you not want to call option b) a computer model, but options c) and d) fully correspond to this name?

Under computer model often understand a program (or a program plus a special device) that provides an imitation of the characteristics and behavior of a particular object. The result of executing this program is also called a computer model.

In the specialized literature, the term "computer model" is more strictly defined as follows:

A conditional image of an object or some system of objects (processes, phenomena), described using interconnected computer tables, flowcharts, diagrams, graphs, drawings, animation fragments, hypertexts, and so on, and displaying the structure (elements and relationships between them) of the object. Computer models of this kind are called structural and functional;

A separate program or a set of programs that, using a sequence of calculations and a graphical display of their results, reproduces (simulates) the processes of the object's functioning under the influence of various, usually random, factors. Such models are called imitation.

Computer models can be simple or complex. You created simple models many times when you learned programming or built your database. In 3D graphics systems, expert systems, automated control systems, very complex computer models are built and used.

Example. The idea of constructing a model of human activity with the help of a computer is not new, and it is difficult to find a field of activity in which it would not be tried to be implemented. Expert systems - computer programs, modeling the actions of a human expert when solving problems in any subject area based on the accumulated knowledge that makes up the knowledge base. ES solve the modeling problem mental activity. Due to the complexity of the models, the development of ES, as a rule, takes several years.

Modern expert systems, in addition to the knowledge base, also have a base of precedents - for example, the results of a survey of real people and information about the subsequent success / failure of their activities. For example, the use case base expert system New York Police - 786 000 people, Center "Hobby" (personnel policy at the enterprise) - 512 000 people, and according to the specialists of this center, the ES developed by them worked with the expected accuracy only when the base exceeded 200 000 man, it took 6 years to create it.

Example. Progress in the creation of computer graphics has moved from wireframe images of three-dimensional models with a simple halftone image to modern realistic pictures that are examples of art. This was the result of success in defining the modeling environment more precisely. Transparency, reflection, shadows, lighting patterns and surface properties are some of the areas where research teams are working hard, constantly coming up with new algorithms to create increasingly realistic artificial images. Today, these methods are also used to create high-quality animation.

practical needs V computer modeling pose challenges for hardware developers funds computer. That is, the method actively influences not only the emergence of new and new programs But And on development technical means.

Example. For the first time, computer holography was discussed in the 80s. So, in computer-aided design systems, in geographic information systems, it would be nice to be able not only to see the object of interest in a three-dimensional form, but to present it in the form of a hologram that can be rotated, tilted, look inside it. To create a holographic image that is useful in real applications, you need

holographic

Pictures

displays with a gigantic number of pixels - up to a billion. Now such work is actively carried out. Simultaneously with the development of the holographic display, work is in full swing on the creation of a three-dimensional workstation based on a principle called "substitution of reality." Behind this term is the idea of wide application of all those natural and intuitive methods that a person uses when interacting with natural (material-energy) models, but at the same time, emphasis is placed on their comprehensive improvement and development using the unique capabilities of digital systems. It is assumed, for example, that it will be possible to manipulate and interact with computer holograms in real time using gestures and touches.

Computer simulation has the following advantages:

Provides visibility;

Available to use.

The main advantage of computer simulation is that it allows not only to observe, but also to predict the result of an experiment under some special conditions. Thanks to this possibility, this method has found application in biology, chemistry, sociology, ecology, physics, economics and many other fields of knowledge.

Computer modeling is widely used in teaching. With the help of special programs, you can see models of such phenomena as the phenomena of the microcosm and the world with astronomical dimensions, the phenomena of nuclear and quantum physics, the development of plants and the transformation of substances in chemical reactions.

The training of specialists of many professions, especially such as air traffic controllers, pilots, nuclear and power plant dispatchers, is carried out with the help of simulators controlled by a computer that simulates real situations, including emergency ones.

Laboratory work can be carried out on a computer if there are no necessary real devices and instruments, or if the solution of a problem requires the use of complex mathematical methods and labor-intensive calculations.

Computer modeling makes it possible to "revive" the studied physical, chemical, biological, social laws, to put a series of experiments with the model. But do not forget that all these experiments are of a very conditional nature and their cognitive value is also very conditional.

Example. Prior to the practical use of the nuclear fission reaction, nuclear physicists simply did not know about the dangers of radiation, but the first mass application of "achievements" (Hiroshima and Nagasaki) clearly showed how much radiation

is dangerous to humans. Start physics with nuclear electro-

stations, humanity would not have learned about the dangers of radiation for a long time. The achievement of chemists at the beginning of the last century - the most powerful pesticide DDT - was considered absolutely safe for humans for a long time -

In the context of the use of powerful modern technologies, wide replication and thoughtless use of erroneous software products, such highly specialized, it would seem, questions, such as the adequacy of a computer model of reality, can acquire significant universal significance.

Computer experiments- it is a tool for studying patterns, not natural or social phenomena.

Therefore, a full-scale experiment should always be carried out simultaneously with a computer experiment, so that the researcher, comparing their results, can evaluate the quality of the corresponding model, the depth of our understanding of the essence of phenomena.

childbirth. Do not forget that physics, biology, astronomy, computer science are sciences about the real world, and not about virtual reality.

IN scientific research, both fundamental and practically directed (applied), the computer often acts as a necessary tool for experimental work.

A computer experiment is most often associated with:

With complex mathematical calculations (number
lazy modeling);

With the construction and study of visual and / or dynamic
mic models (computer modelling).

Under computer model refers to a program (or a program in conjunction with a special device) that provides an imitation of the characteristics and behavior of a particular object, as well as the result of the execution of this program in the form of graphic images (stationary or dynamic), numerical values, tables, etc.

There are structural-functional and simulation computer models.

Structural-functional a computer model is a conditional image of an object or some system of objects (processes, phenomena), described using interconnected computer tables, flowcharts, diagrams, graphs, drawings, animation fragments, hypertexts, and so on, and displaying the structure of an object or its behavior.

A simulation computer model is a separate program or software package that allows, using a sequence of calculations and a graphical display of their results, to reproduce (simulate) the processes of an object's functioning under the influence of various random factors.

Computer modeling is a method for solving the problem of analyzing or synthesizing a system (most often a complex system) based on the use of its computer model.

Advantages of computer simulation are that it:

Allows not only to observe, but also to predict the result of the experiment under some special conditions;

Allows you to model and study the phenomena predicted by any theories;

It is environmentally friendly and does not pose a danger to nature and humans;

Provides visibility;

Available to use.

The computer modeling method has found application in biology, chemistry, sociology, ecology, physics, economics, linguistics, jurisprudence and many other fields of knowledge.

Computer modeling is widely used in education, training and retraining of specialists:

For a visual representation of models of the phenomena of the microworld and the world with astronomical dimensions;

To simulate the processes occurring in the world of animate and inanimate nature

To simulate real situations of complex systems management, including emergencies;

For laboratory work when there are no necessary devices and devices;

For solving problems, if this requires the use of complex mathematical methods and labor-intensive calculations.

It is important to remember that it is not objective reality that is modeled on a computer, but our theoretical ideas about it. The object of computer modeling are mathematical and other scientific models, and not real objects, processes, phenomena.

Computer experiments- it is a tool for studying patterns, not natural or social phenomena.

The criterion of fidelity of any of the results of computer simulation has been and remains a full-scale (physical, chemical, social) experiment. In scientific and practical research, a computer experiment can only accompany a full-scale one, so that the researcher can compare

Nivaya their results, could assess the quality of the model, the depth of our ideas about the essence of natural phenomena.

It is important to remember that physics, biology, astronomy, economics, computer science are sciences about the real world, and not about
virtual reality.

Exercise 1

A letter written in a text editor and sent to e-mail, hardly anyone would call a computer model.

Text editors often allow you to create not only ordinary documents (letters, packs, reports), but also document templates in which there is constant information that the user cannot change, there are data fields that are filled in by the user, and there are fields in which calculations based on the entered data. Can such a template be considered as a computer model? If so, what is the object of modeling in this case and what is the purpose of creating such a model?

Task 2

You know that before you create a database, you first need to build a data model. You also know that an algorithm is a model of activity.

Both data models and algorithms are most often developed with computer implementation in mind. Can we say that at some point they become a computer model, and if so, when does this happen?

Note. Check your answer against the definition of "computer model".

Task 3

Describe the stages of building a computer model using the example of developing a program that simulates some physical phenomenon.

Task 4

Give examples of when computer simulation has brought real benefits and when it has led to undesirable consequences. Prepare a report on this topic.

The leading practical teaching methods are exercise, experiments and experimentation, modeling

Question 11. The method of social experiment, its advantages and disadvantages

CHAPTER 2

In conclusion of the chapter, we consider the question: where to attribute a computer experiment and computer simulation ( computer simulations) !

Initially, computer modeling appears in meteorology and nuclear physics, but today the range of its application in science and technology is extremely wide. In this regard, the example of "global modeling" is very indicative, where the world is viewed as a set of interacting subsystems: population, society, economy, food production, innovation complex, Natural resources, habitat, countries and regions of the world (the first example is the report published in 1972 to the Club of Rome "Limits to Growth"). The development and interaction of these subsystems determine the world dynamics.

Obviously, we are dealing here with a supercomplex system with a lot of nonlinear interactions, for which unable to build a VIO model type. Therefore, here proceed as follows. A multidisciplinary group is assembled, consisting of specialists belonging to various subsystems. This group, based on the knowledge of its members, makes up a block diagram of a large number of elements and relationships. This block diagram is converted into a mathematical computer model representing the system being modeled. After that, numerical experiments are carried out with a computer model, i.e. computer experiments that, from the side of creating models of objects and processes, debugging and execution, resemble a real complex experiment.

There is a certain analogy between thought and computer experiments. In the case of a computer experiment, the computer model worked out in the course of it is an analogue of the FIE model in a mental FIE experiment. In both cases pilot study is an element of the search for an adequate theoretical model. In the course of this search, in the first case, FECs and interactions between them (and their value) are selected, and in the second case, elements and relationships (and their value). From this comparison it is obvious that in both cases the emergence of new knowledge is possible as a result of such experimental activity. That is, the computer models correspond to the theoretical RES models of the phenomenon, and the computer experiment is a tool for their construction. In this case, experimentation takes place with the model, and not with the phenomenon (according to the work, the same is indicated in the works).

In physics and other natural sciences, in the case of "laboratory" phenomena, a real experiment can change something in the phenomenon itself ("ask it a question"). If this turns out to be enough to create a VIO model, and the only question remains about refining its parameters, then in this case the computer model has a more trivial application than described above - solving complex equations that describe a physical or technical system, and selecting parameters for systems for which the VIO model is already defined. This case is often referred to as a "numerical experiment".

However, physics also considers phenomena that need to be qualitatively studied before they are placed in the laboratory, for example, the release of nuclear energy or the birth of elementary particles. A similar situation may arise: 1) in the cases of economic or technical complexity of a real experiment listed for a thought experiment, 2) in the absence of a PRI model, i.e. the absence of a theory of the phenomenon (as in the case of turbulent flows). In nuclear physics and particle physics we have the first if not both cases. Here we have a situation similar to "global simulation" and start experimenting with theoretical models through computer simulations. Therefore, it is not surprising that computer simulation appeared very early in nuclear physics.

So, a computer experiment and computer models in a non-trivial case, as in the "global simulation" example, correspond, respectively, to a mental RES experiment and theoretical RES models of the phenomenon.

An experiment is a form of communication between two sides - a phenomenon and a theoretical model. In principle, this implies the possibility of manipulation with two sides. In the case of a real experiment, experimentation occurs with a phenomenon, and in the case of a mental and computer experiment, which can be considered as an analogue of a mental one, with a model. But in both cases, the goal is to obtain new knowledge in the form of an adequate theoretical model.

This includes E. Winsberg's remark: "It is not true that a real experiment always manipulates only the object of interest. In fact, both in a real experiment and in a simulation, there is a complex relationship between what is manipulated in the study, on the one hand, and world, which are the goal of the study - on the other ... Mendel, for example, manipulated peas, but was interested in studying the phenomenon of general heredity ".

A computer experiment with a system model during its research and design is carried out in order to obtain information about the characteristics of the process of functioning of the object under consideration. The main task of planning computer experiments is to obtain the necessary information about the system under study under resource constraints (computer time, memory, etc.). Among the particular tasks solved when planning computer experiments are the tasks of reducing the cost of computer time for modeling, increasing the accuracy and reliability of modeling results, checking the adequacy of the model, etc.

The effectiveness of computer experiments with models significantly depends on the choice of the experimental plan, since it is the plan that determines the volume and procedure for performing calculations on a computer, methods for accumulating and statistical processing of system simulation results. . Therefore, the main task of planning computer experiments with a model is formulated as follows: it is necessary to obtain information about the object of modeling, given in the form of a modeling algorithm (program), with minimal or limited expenditure of machine resources for the implementation of the modeling process.

The advantage of computer experiments over natural ones is the ability to fully reproduce the conditions of the experiment with the model of the system under study. . A significant advantage over full-scale ones is the ease of interrupting and resuming computer experiments, which makes it possible to apply sequential and heuristic planning techniques that may not be feasible in experiments with real objects. When working with a computer model, it is always possible to interrupt the experiment for the time necessary to analyze the results and make decisions about its further course (for example, on the need to change the values of the model characteristics).

The disadvantage of computer experiments is that the results of some observations depend on the results of one or more previous ones, and therefore they contain less information than independent observations.

In relation to the database, a computer experiment means the manipulation of data in accordance with the set goal using the tools of the DBMS. The purpose of the experiment can be formed based on the general purpose of the simulation and taking into account the requirements of a particular user. For example, there is a database "Dean's office". common goal creating this model - management educational process. If you need to obtain information about the progress of students, you can make a request, i.e. conduct an experiment to select the desired information.

The DBMS environment toolkit allows you to perform the following operations on data:

1) sorting - ordering data according to some attribute;

2) search (filtering) - selection of data that satisfies a certain condition;

3) creation of calculation fields - transformation of data into another form based on formulas.

Information model management is inextricably linked with the development of various criteria for searching and sorting data. Unlike paper filing cabinets, where sorting is possible according to one or two criteria, and the search is generally carried out manually - by sorting through cards, computer databases allow you to set any sorting forms for various fields and various search criteria. The computer will sort or select the necessary information without time expenditure according to the given criterion.

For successful work with the information model, database software environments allow you to create calculation fields in which the original information is converted into a different form. For example, according to grades in a semester, using a special built-in function, you can calculate GPA student achievement. Such calculation fields are used either as Additional Information, or as a criterion for searching and sorting.

A computer experiment includes two stages: testing (checking the correctness of operations) and conducting an experiment with real data.

After formulating formulas for calculated fields and filters, you need to make sure that they work correctly. To do this, you can enter test records for which the result of the operation is known in advance.

The computer experiment ends with the output of the results in a form convenient for analysis and decision making. One of the advantages of computer information models is the ability to create various forms of presentation of output information, called reports. Each report contains information that meets the purpose of a particular experiment. The convenience of computer reports lies in the fact that they allow you to group information according to given criteria, enter the final fields for counting records by group and in general for the entire database, and then use this information to make a decision.

The environment allows you to create and store several typical, frequently used report forms. Based on the results of some experiments, you can create a temporary report that is deleted after copying it to a text document or printing. Some experiments do not require reporting at all. For example, it is required to select the most successful student for assignment higher scholarship. To do this, it is enough to sort by the average score of grades in the semester. The required information will contain the first entry in the list of students.