Asymptotic Solution of Singularly Pertubeted Problems withQuadratic Small Parameter

Abstract

In this paper we study singularly perturbed with initial problem of the systemwithtwo linear ordinary differential equations, each ofwhich 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 intervalsolution 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.