Asymptotic solution of singularly pertubeted problems with quadratic small parameter

Abstract EN

In this paper we study singularly perturbed with initial problem of the system with two linear ordinary differential equations, each of which contains small parameter in its derivative and quadratic the same small parameter in one of them.

A uniform asymptotic expansion is constructed on a time interval solution of the problem.

obtained formulas for the terms of internal expansion, they allow us to find them only through algebraic operations, finally we give examples which related with our subject.