1. Mathematical modeling

Simulation - replacement of the object (the original) in its conventional way (model) and study the properties of the original by studying the properties of the model. There are physical and mathematical models.

Mathematical model - a set of mathematical relations, equations, inequalities, describing the basic laws of the object under study.

Natural phenomena, production process, economics, etc.

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Formalization, mathematical model

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Search, solution

The mathematical model is based on some simplification (idealization) and is an approximate description of reality.

An analysis of a mathematical model allows predicting the behavior of a real object.

Mathematical models are widely used in physics, biology, and the like.

The model is never the same as the real process. The results of the mathematical model only approximate the process.

A criterion for adequacy (matching) of a mathematical model and a real process is practice (field experiment).

The formal classification of models is based on the mathematical tools used to solve the tasks.

There are models:

  • Linear or nonlinear models;
  • Concentrated or distributed systems;
  • Deterministic or stochastic;
  • Static or dynamic.

Simulation (simulation) involves presenting a model in the form of an algorithm and a computer program that allows you to recreate the behavior of the object.

Imitation models are considered as experiments conducted on computers, with mathematical models simulating the behavior of real objects.

At the same time, elementary phenomena are simulated with the preservation of their logical structure and consistency in time, which allows obtaining information about the state of the system at a certain point in time and evaluate the characteristics of the system.

Imitation models allow solving more complex tasks than analytic ones.