Algorithm of the Regularization Method for a Nonlinear Singularly Perturbed Integro-Differential Equation with Rapidly Oscillating Inhomogeneities

Abdukhafiz Abdurasulovich Bobodzhanov, Burkhan T. Kalimbetov, В. Ф. Сафонов

2022

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DOI 10.1134/s0012266122030090
Data confidence 70 medium
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Abstract

Abstract Lomov’s regularization method is generalized to nonlinear singularly perturbed integro-differential equations with rapidly oscillating right-hand side. The influence of the kernel of the integral operator, the nonlinearity, and the rapidly oscillating part on the asymptotics of the solution of the initial value problem for these equations is established. Previously, singularly perturbed linear systems of this type and nonlinear systems without oscillating inhomogeneity were studied.