Stability criteria of systems of nonlinear ordinary differential equations based on additive transformations of the formula of finite increments

S. G. Bulanov

A.P. Chekhov Taganrog Institute (branch) of Rostov State Economical University

Abstract: Based on additive transformations of difference schemes and the formula of finite increments, we obtain criteria for the Lyapunov stability of systems of ordinary differential equations. The mathematical structure of the criteria admits the possibility of software implementation. Approximate solutions of the system can be computed by the piecewise interpolation method with iterative refinement. The search for Lagrange points is based on calculating the minimum of the modulus function using the sorting by stable address merging. Practical applications of the criteria allow one to perform the stability analysis in real-time mode.

Keywords: Lyapunov stability, computer stability analysis, numerical modeling of stability

UDC: 517.91:519.6

MSC: 34D20

DOI: 10.36535/2782-4438-2025-241-3-12