Asymptotics solving singularly perturbed integro-differential systems with parametric amplification

Abstract

The initial value problem for a singularly perturbed integro-differential systems with rapidly oscillating coefficients. For asymptotic integration of the original problem, a modification of the method proposed regularization S.A.Lomov. The essence of modification is to introduce along with additional independent variables associated with rapidly oscillating coefficients and variables, taking into account the essential singular singularities that are involved in solving of the original problem. Justified procedure for constructing general member asymptotic solution of problem, which in absence of an integral member coincides with general member asymptotic solution of the differential system.