Algorithm of the Regularization Method for a Singularly Perturbed Integro-differential Equation with a Rapidly Decreasing Kernel and Rapidly Oscillating Inhomogeneity

被引：3
|
作者：
Bobodzhanov, Abdukhafiz A. [1 ]
Kalimbetov, Burkhan T. [2 ]
Safonov, Valeriy F. [1 ]
机构：
[1] Natl Res Univ, Moscow Power Engn Inst, Moscow, Russia
[2] Akhmet Yassawi Int Kazakh Turkish Univ, Turkestan, Kazakhstan
来源：
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS | 2022年 / 15卷 / 02期
关键词：
singular perturbation; integro-differential equation; rapidly oscillating right-hand side; rapidly varying kernel; regularization; solvability of iterative problems; DIFFERENTIAL-EQUATIONS; ASYMPTOTIC SOLUTIONS;
D O I：
10.17516/1997-1397-2022-15-2-214-223
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：214 / 223
页数：10
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