The stability analysis of nonlinear differential equations systems based on linearization and multiplicative transformations of difference schemes.
Bulanov S.G., Ilyuhin
It is proposed approach to the stability analysis of nonlinear system of ordinary differential equation (ODE) on the basis of linearization in the neighborhood of the studied solutions. On this basis, and using multiplicative transformations of difference schemes the method of the numerical computer analysis of stability of nonlinear systems is constructed. Computer implementation of the scheme allows to unambiguously determine the nature of stability, asymptotic stability or instability of nonlinear systems of ODE without presenting the solution in an analytical form. A variation of scheme which uses analytical solutions is given. The codes and results of the numerical experiment are presented.Keywords: Computer simulation of stability; differential solutions differential equations; Lyapunov stability.
