Holomorphic Regularization of Singularly Perturbed Integro-Differential Equations

Abstract

S.A. Lomov’s regularization method has long been used to solve integro-differential singularly perturbed equations, which are very important from the viewpoint of applications. In this method, the series in powers of a small parameter representing the solutions of these equations converge asymptotically. However, in accordance with the main concept of the method, to construct a general singular perturbation theory one must indicate conditions for the ordinary convergence of these series. This is the subject of the present paper.