### Chirkunov Y.A.

## New algorithm of group classification of systems of differential equations

NEW ALGORITHM OF GROUP CLASSIFICATION OF SYSTEMS OF DIFFERENTIAL EQUATIONS

Chirkunov Yu. A.

Institute of Computationals Technologies, Novosibirsk, Russia

Novosibirsk State Technical University, Novosibirsk, Russia

chr01@rambler.ru

Differential equations of mechanics and mathematical physics often contain include parameters and functions defined with the help of experiments. It’s parameters and functions are an arbitrary element of these equations. Group classification of it’s equations permits to obtain values and forms of these parameters and functions guarantee existence of additional symmetries of considered mathematical models. Models admitting additional symmetries as a rule are the most perspective for mathematical research.

We offer a new algorithm of group classification of system of differential equations. Efficiency and preferences of it’s algorithm are illustrated with a help of gas dynamics equations and equations of nonlinear longitudinal oscillations of visco-elastic rod in Kelvin’s model. A new algorithm has following possess an advantages over classical algorithm [1]: 1) there is no necessity to solve difficult problems connected with classifying equations; 2) volume of calculations is essentially reduced; 3) group of equivalences is found at once for every particular arbitrary element.

REFERENCES

1. L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978) [in Russia].

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