Geodesic
Modelling of Lyapunov stability based on processing of the difference solutions of ordinary difference equations
Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 105-118.

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The schemes for computer analysis of solution stability of ordinary differential equations systems are presented. The schemes are based on difference solutions transformations that are made simultaneously with stability assessment real-time. In general case the transformation of the second member function isn't performed, characteristic quantity calculations are not required for linear systems, in the case of matrix of constant coefficients the information about characteristic polynomial and its roots isn't used. 
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Ya. E. Romm. Modelling of Lyapunov stability based on processing of the difference solutions of ordinary difference equations. Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 105-118. http://geodesic.mathdoc.fr/item/MM_2008_20_12_a7/

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