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

Bibulova D. Kalimbetov B. Safonov V.
2025 Diogenes Co. Ltd.

International Journal of Applied Mathematics
2025 #38 Issue 2s 647 - 671 pp.

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 ker-nel. 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.

iterative problem , rapidly changing kernel , rapidly oscillating inhomogeneity , regularization , singularly perturbation

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M. Auezov South Kazakhstan University, Tauke-xan 5, Shymkent, 160000, Kazakhstan
A. Kuatbekov Peoples’ Friendship University, Tole bi 32b, Shymkent, 160011, Kazakhstan
The National Research University, MPEI, Krasnokazarmennaya 14, Moscow, 111250, Russian Federation

M. Auezov South Kazakhstan University
A. Kuatbekov Peoples’ Friendship University
The National Research University

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