Introduction
At present, to study complex processes and systems, along with a full-scale
experiment, a computational experiment is used—a methodology based on the
application of applied mathematics and computer technology, combining the
advantages of both theory and experiment. A computational experiment has a
number of indisputable advantages over a full-scale one. The main specificity of the
computational experiment (computer simulation) is the ability to virtually predict
the properties of the object being modeled, depending on the various conditions of
its operation and variable design parameters. In addition, for the study of complex
objects and systems, computational experiment is less expensive, and its implementation requires significantly less time. In addition, it can predict the results of
critical tests, which may, in reality, lead to the loss of the full-scale object under
investigation. A computational experiment acquires exceptional importance in
those cases when full-scale experiments or physical model experiments are
impossible. The adequacy of computer simulation results is determined by the
credibility of the employed mathematical model which describes the system or
process with a given accuracy.
The construction of a mathematical model that allows to obtain correct results in
the process of computer simulation includes the following steps:
– building a model that involves the separation of all factors acting in the phenomenon under consideration into major and minor factors, the latter is not
accounted for at the initial stage of research; formulation of assumptions and
conditions of applicability of the model; determination of the boundaries in
which the results would be fair; describing the model in mathematical terms,
usually, in the form of differential or integro-differential equations;
– development (selection) of a method for solving a posed mathematical problem.
When building a method for solving a problem, the accuracy and efficiency
of the numerical methods used for calculation are important;
– development of an algorithm for solving the problem. When implementing this
stage, it should be remembered that the accuracy of calculations on a computer
is limited; in addition, any method of calculation also introduces an error.
ix
At present, to study complex processes and systems, along with a full-scale
experiment, a computational experiment is used—a methodology based on the
application of applied mathematics and computer technology, combining the
advantages of both theory and experiment. A computational experiment has a
number of indisputable advantages over a full-scale one. The main specificity of the
computational experiment (computer simulation) is the ability to virtually predict
the properties of the object being modeled, depending on the various conditions of
its operation and variable design parameters. In addition, for the study of complex
objects and systems, computational experiment is less expensive, and its implementation requires significantly less time. In addition, it can predict the results of
critical tests, which may, in reality, lead to the loss of the full-scale object under
investigation. A computational experiment acquires exceptional importance in
those cases when full-scale experiments or physical model experiments are
impossible. The adequacy of computer simulation results is determined by the
credibility of the employed mathematical model which describes the system or
process with a given accuracy.
The construction of a mathematical model that allows to obtain correct results in
the process of computer simulation includes the following steps:
– building a model that involves the separation of all factors acting in the phenomenon under consideration into major and minor factors, the latter is not
accounted for at the initial stage of research; formulation of assumptions and
conditions of applicability of the model; determination of the boundaries in
which the results would be fair; describing the model in mathematical terms,
usually, in the form of differential or integro-differential equations;
– development (selection) of a method for solving a posed mathematical problem.
When building a method for solving a problem, the accuracy and efficiency
of the numerical methods used for calculation are important;
– development of an algorithm for solving the problem. When implementing this
stage, it should be remembered that the accuracy of calculations on a computer
is limited; in addition, any method of calculation also introduces an error.
ix