Geodesic
Algorithm of the regularization method for a singularly perturbed integro-differential equation with a rapidly decreasing kernel and rapidly oscillating inhomogeneity
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 216-225

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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 rapidly varying kernel. The main goal of this work is to generalize the Lomov's regularization method and to reveal the influence of the rapidly oscillating right-hand side and a rapidly varying kernel on the asymptotics of the solution to the original problem.
Keywords: integro-differential equation, rapidly oscillating right-hand side, rapidly varying kernel, regularization, solvability of iterative problems.
Mots-clés : singular perturbation 
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     title = {Algorithm of the regularization method for a singularly perturbed integro-differential equation with a rapidly decreasing kernel and rapidly oscillating inhomogeneity},
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Abdukhafiz A. Bobodzhanov; Burkhan T. Kalimbetov; Valeriy F. Safonov. Algorithm of the regularization method for a singularly perturbed integro-differential equation with a rapidly decreasing kernel and rapidly oscillating inhomogeneity. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 216-225. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a7/