Computer algebra methods in the study of nonlinear differential systems

Authors:
V. D. Irtegov;T. N. Titorenko
Affiliations:
Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia 664033;Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia 664033
Venue:
Computational Mathematics and Mathematical Physics
Year:
2013

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Abstract

Some issues concerning computer algebra methods as applied to the qualitative analysis of differential equations with first integrals are discussed. The problems of finding stationary sets and analyzing their stability and bifurcations are considered. Special attention is given to algorithms for finding and analyzing peculiar stationary sets. It is shown that computer algebra tools, combined with qualitative analysis methods for differential equations, make it possible not only to enhance the computational efficiency of classical algorithms, but also to implement new approaches to the solution of well-known problems and, in this way, to obtain new results.