1.1 Basic Modeling Concepts
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Imitational modeling is a type of computer simulation, which is characterized by
reproduction on a computer (imitation) of the process of functioning of the system
under study. This simulates the elementary phenomena that make up the process,
while preserving their logical structure and the sequence of flow in time, which
allows to obtain information about the state of the system at specified points in time.
Statistical modeling is a type of computer simulation that allows to obtain
statistical data on the processes in the simulated system.
The stages of computer simulation are: model development, algorithm development, and software implementation.
At the first stage, an “equivalent” object is built. This “equivalent” reflects in a
mathematical form, the properties of an object that are important for a given study:
the laws to which the object obeys, the connections inherent in its parts, etc. This
stage is characterized by the principle of decomposition, that is, the division of
the original object into separate elements and the mathematical description of each
element. Then, the mathematical model can be investigated by theoretical methods,
which allows one to obtain preliminary knowledge about the object.
The second stage is the development of an algorithm for implementing the model
on a computer. The model is presented in a form convenient for the application of
numerical methods, and the sequence of computational and logical operations that
need to be performed is determined in order to find the desired quantities with a
given accuracy. Computational algorithms should not distort the basic properties of
the model and, consequently, the original object, should be economical, and should
adapt to the peculiarities of the tasks and computers used.
At the third stage, programs are created that “translate” the model and algorithm
into a language accessible to a computer. They are also subject to the requirements
of efficiency and adaptability. They can be called the “electronic” equivalent of the
object being studied, already suitable for testing on a computer.
The method of computer simulation combines the advantages of theory and experiment. Indeed, working not with the object itself (a phenomenon or process), but with
a computer model, makes it possible to investigate its properties relatively quickly,
without significant expenses. This constitutes the advantages of the theory. At the
same time, computational experiments with models of objects make it possible,
based on the power of computational methods and computers, to study objects in
great breadth and depth, which is inaccessible by purely theoretical approaches. This
already constitutes the advantages of the experiment.
1.2 Classification of Mathematical Models
Mathematical models are distinguished by the nature of the displayed properties of
the system, their degree of detail, methods of derivation, and formal presentation.
By the way of presenting the system, the models are divided into structural and
functional. If the mathematical model reflects the structure of the simulated system,
that is, it highlights the elements and their system connections, then it is called
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Imitational modeling is a type of computer simulation, which is characterized by
reproduction on a computer (imitation) of the process of functioning of the system
under study. This simulates the elementary phenomena that make up the process,
while preserving their logical structure and the sequence of flow in time, which
allows to obtain information about the state of the system at specified points in time.
Statistical modeling is a type of computer simulation that allows to obtain
statistical data on the processes in the simulated system.
The stages of computer simulation are: model development, algorithm development, and software implementation.
At the first stage, an “equivalent” object is built. This “equivalent” reflects in a
mathematical form, the properties of an object that are important for a given study:
the laws to which the object obeys, the connections inherent in its parts, etc. This
stage is characterized by the principle of decomposition, that is, the division of
the original object into separate elements and the mathematical description of each
element. Then, the mathematical model can be investigated by theoretical methods,
which allows one to obtain preliminary knowledge about the object.
The second stage is the development of an algorithm for implementing the model
on a computer. The model is presented in a form convenient for the application of
numerical methods, and the sequence of computational and logical operations that
need to be performed is determined in order to find the desired quantities with a
given accuracy. Computational algorithms should not distort the basic properties of
the model and, consequently, the original object, should be economical, and should
adapt to the peculiarities of the tasks and computers used.
At the third stage, programs are created that “translate” the model and algorithm
into a language accessible to a computer. They are also subject to the requirements
of efficiency and adaptability. They can be called the “electronic” equivalent of the
object being studied, already suitable for testing on a computer.
The method of computer simulation combines the advantages of theory and experiment. Indeed, working not with the object itself (a phenomenon or process), but with
a computer model, makes it possible to investigate its properties relatively quickly,
without significant expenses. This constitutes the advantages of the theory. At the
same time, computational experiments with models of objects make it possible,
based on the power of computational methods and computers, to study objects in
great breadth and depth, which is inaccessible by purely theoretical approaches. This
already constitutes the advantages of the experiment.
1.2 Classification of Mathematical Models
Mathematical models are distinguished by the nature of the displayed properties of
the system, their degree of detail, methods of derivation, and formal presentation.
By the way of presenting the system, the models are divided into structural and
functional. If the mathematical model reflects the structure of the simulated system,
that is, it highlights the elements and their system connections, then it is called