ALGORITHM OF THE REGULARIZATION METHOD FOR A SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL SYSTEM WITH A RAPIDLY VARIABLE KERNEL AND WITH RAPIDLY OSCILLATING INHOMOGENEITIES

Abstract

In this paper, we consider a singularly perturbed integro- differential system with a rapidly oscillating right-hand side, including an integral operator with a rapidly changing kernel. Earlier, a singularly perturbed integro-differential system with a rapidly oscillating inhomogeneity and with a slowly varying kernel was studied. The main goal of this work is to generalize the Lomov regularization method and to reveal the influence of a rapidly oscillating right-hand side and a rapidly changing kernel on the asymptotics of the solution to the original problem.