# Synthesis of Adequate Mathematical Description as Solution of Special Inverse Problems

### Abstract

The problem of mathematical simulation of dynamic system characteristics behavior andÂ their adequacy to real experimental data, which correspond to these characteristics, is considered inÂ this paper. The specified problem is still poorly investigated and hardly adapted to formalization. TheÂ requirements of related to the adequate mathematical simulation of dynamic system are considered forÂ the case when mathematical description is represented by system of the ordinary differential equations.Â The conditions are obtained which allow to reduce a problem of the adequate mathematical descriptionÂ to the solution of the several integral equations of the first type. The methods of obtaining of the steadyÂ solutions are suggested. The domains of application of the obtained solutions are specified. For a case,Â when the differential equations of dynamic system are given with errors in coefficients, several variantsÂ of synthesis of the adequate mathematical descriptions depending on final goals of this description useÂ are suggested. The examples of the adequate descriptions of concrete dynamic systems are given.

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