The Study of Splitting Method of Singularly Perturbed Initial Value Problems for Non-Autonomous Systems of ODE

Abstract

With the help of non-autonomous version of the method of Splitting with new point of view, the paper studied singularly perturbed initial value problems for model systems of ODE. The proposed method will allow us to construct quasi-regular asymptotic solutions for linear Cauchy Problems and to formulate criteria for the stability of singularly perturbed quasi-linear problems.