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Computer-Oriented Stability Analysis Based on Recurrent Transformation of Difference Solutions of Ordinary Differential Equations

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Abstract

Criteria for the Lyapunov stability of solutions to systems of ordinary differential equations are presented in the difference, additive, and integral forms. They contain the necessary and sufficient conditions and do not transform functions in the right-hand side of the system. In general, the criteria are intended for computer implementation, and some of them for analytical research. Based on the comparison of the integrands, the stability of some systems of nonlinear equations is analyzed without a priori solutions. The programmed criteria are given for general systems, examples and results of program and numerical experiments are presented.

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Authors and Affiliations

  1. A. P. Chekhov State Pedagogical Institute, Taganrog, Russia

    Ya. E. Romm

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  1. Ya. E. Romm
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Correspondence to Ya. E. Romm.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2015, pp. 107–124.

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Romm, Y.E. Computer-Oriented Stability Analysis Based on Recurrent Transformation of Difference Solutions of Ordinary Differential Equations. Cybern Syst Anal 51, 416–431 (2015). https://doi.org/10.1007/s10559-015-9733-x

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