Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine

Abdukhafiz Abdurasulovich Bobodzhanov, Burkhan T. Kalimbetov, N. A. Pardaeva

2023

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DOI 10.22436/jmcs.032.01.07
Data confidence 70 medium
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Abstract

In this paper, we consider a singularly perturbed integro-differential equation with a rapidly oscillating right-hand side, which includes an integral operator with a slowly varying kernel. Earlier, singularly perturbed differential and integro-differential equations with rapidly oscillating coefficients were considered. The main goal of this work is to generalize the Lomov's regularization method and to identify the rapidly oscillating right-hand side to the asymptotics of the solution to the original problem.