6
1 Modeling Systems
The cost-effectiveness of a mathematical model is estimated by the cost of computing resources (machine time and memory) necessary to implement a mathematical
model on a computer. These costs depend on the number of arithmetic operations
when using the model, on the dimension of the space of phase variables and other
factors.
1.4 Computer Simulation and Computational Experiment
Most mathematical models of practical interest are very complex and do not allow
to obtain a solution in analytical form. Solutions for such models are built using
mathematical packages that allow performing symbolic calculations. A model built
in this way is called a computer. Computer modeling consists in the development of an
algorithm (program) describing a model of the system under study. As noted earlier,
computer modeling allows you to repeatedly reduce the cost of developing models
compared to non-computer modeling methods and conducting full-scale tests. The
creation of a computer model is usually done on the basis of a mathematical one.
Thus, computer modeling can be considered as a kind of mathematical modeling.
The computer model must have all the properties of the mathematical model listed
above. It should, if possible, reflect all the basic qualities, factors, and relationships
that characterize the system, as well as the criteria and restrictions imposed on it. That
is, the model should be sufficiently universal to adequately describe the simulated
system. On the other hand, to perform the necessary research at a reasonable cost, the
model should be relatively simple. These two requirements suggest that computer
modeling of systems is an art rather than an established science.
The essence of computer simulation lies in obtaining quantitative and qualitative
results for the developed model. Computer modeling is a tool that allows you to obtain
quantitative results and make qualitative conclusions that allow one to detect previously unknown properties of a complex system: its structure, development dynamics,
stability, integrity, and other.
The process of building computer models can be represented as a sequence of the
following steps.
1. Problem statement and its analysis. At this stage, the objectives of the simulation
are determined, and the initial information about the system is collected.
2. Construction of a mathematical model. The essential parameters of the model and
the relationship between them are determined, and a mathematical description
of the dependencies between the parameters is made.
3. Development and implementation of a computer model algorithm. The method
of obtaining the initial data is determined, the algorithm is compiled, and its correctness is checked. Next, the tools are selected by the algorithm implementation
program, a model is developed, and its correctness is verified.
1 Modeling Systems
The cost-effectiveness of a mathematical model is estimated by the cost of computing resources (machine time and memory) necessary to implement a mathematical
model on a computer. These costs depend on the number of arithmetic operations
when using the model, on the dimension of the space of phase variables and other
factors.
1.4 Computer Simulation and Computational Experiment
Most mathematical models of practical interest are very complex and do not allow
to obtain a solution in analytical form. Solutions for such models are built using
mathematical packages that allow performing symbolic calculations. A model built
in this way is called a computer. Computer modeling consists in the development of an
algorithm (program) describing a model of the system under study. As noted earlier,
computer modeling allows you to repeatedly reduce the cost of developing models
compared to non-computer modeling methods and conducting full-scale tests. The
creation of a computer model is usually done on the basis of a mathematical one.
Thus, computer modeling can be considered as a kind of mathematical modeling.
The computer model must have all the properties of the mathematical model listed
above. It should, if possible, reflect all the basic qualities, factors, and relationships
that characterize the system, as well as the criteria and restrictions imposed on it. That
is, the model should be sufficiently universal to adequately describe the simulated
system. On the other hand, to perform the necessary research at a reasonable cost, the
model should be relatively simple. These two requirements suggest that computer
modeling of systems is an art rather than an established science.
The essence of computer simulation lies in obtaining quantitative and qualitative
results for the developed model. Computer modeling is a tool that allows you to obtain
quantitative results and make qualitative conclusions that allow one to detect previously unknown properties of a complex system: its structure, development dynamics,
stability, integrity, and other.
The process of building computer models can be represented as a sequence of the
following steps.
1. Problem statement and its analysis. At this stage, the objectives of the simulation
are determined, and the initial information about the system is collected.
2. Construction of a mathematical model. The essential parameters of the model and
the relationship between them are determined, and a mathematical description
of the dependencies between the parameters is made.
3. Development and implementation of a computer model algorithm. The method
of obtaining the initial data is determined, the algorithm is compiled, and its correctness is checked. Next, the tools are selected by the algorithm implementation
program, a model is developed, and its correctness is verified.