Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine
Authors
A. Bobodzhanov
- The National Research University, MPEI, Krasnokazarmennaya 14, Moscow, Russia.
B. Kalimbetov
- M. Auezov South Kazakhstan University, Tauke-xan 5, Shymkent, Kazakhstan.
N. Pardaeva
- Almalyk branch of the NRTU MISA, Amir Temur 56, Almalyk, Uzbekistan.
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.
Share and Cite
ISRP Style
A. Bobodzhanov, B. Kalimbetov, N. Pardaeva, Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine, Journal of Mathematics and Computer Science, 32 (2024), no. 1, 74--85
AMA Style
Bobodzhanov A., Kalimbetov B., Pardaeva N., Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine. J Math Comput SCI-JM. (2024); 32(1):74--85
Chicago/Turabian Style
Bobodzhanov, A., Kalimbetov, B., Pardaeva, N.. "Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine." Journal of Mathematics and Computer Science, 32, no. 1 (2024): 74--85
Keywords
- Singular perturbation
- integro-differential equation
- oscillating right-hand side
- solvability of iterative problems
- regularization problems
MSC
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