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Calculation of power expansion solutions of N. Kowalewski modified ODE system by power geometry algorithms

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Abstract

Calculation of power expansion solutions of N. Kowalewski ODE system by power geometry algorithms is continued. N. Kowalewski system is a system of two nonlinear nonautonomous ordinary differential equations. A. Bruno, V. Lunev, and I. Gashenenko used power geometry algorithms to calculate various expansions of solutions of this system in the cases where the independent variable tends to zero or infinity. Now, we consider the cases where the independent variable tends to a nonzero bounded constant. For this purpose, the independent variable is divided into a constant part, which becomes a new parameter, and a new variable, and the solutions are expanded in terms of this new variable. Power expansions of solutions of the system are calculated by power geometry algorithms. The algorithms used are implemented in the language of symbolic calculations Maxima and in C++.

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  1. Scientific Research Institute of Long-Range Radio Communication, 1-ya ul. Bukhvostova 12/11, Moscow, 107258, Russia

    A. B. Aranson

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  1. A. B. Aranson
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Correspondence to A. B. Aranson.

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Original Russian Text © A.B. Aranson, 2011, published in Programmirovanie, 2011, Vol. 37, No. 2.

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Aranson, A.B. Calculation of power expansion solutions of N. Kowalewski modified ODE system by power geometry algorithms. Program Comput Soft 37, 87–98 (2011). https://doi.org/10.1134/S0361768811020034

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  • DOI: https://doi.org/10.1134/S0361768811020034

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