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.

引用

页码：214 / 223

页数：10

共 50 条

[41] A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order
Bobodzhanov, A. A.
Safonov, V. F.
IZVESTIYA MATHEMATICS, 2016, 80 (02) : 285 - 298
[42] The coupled method for singularly perturbed Volterra integro-differential equations
Tao, Xia
Zhang, Yinghui
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
[43] The asymptotic method of differential inequalities for singularly perturbed integro-differential equations
Nefedov, NN
Nikitin, AG
DIFFERENTIAL EQUATIONS, 2000, 36 (10) : 1544 - 1550
[44] A posteriori error estimation for a singularly perturbed Volterra integro-differential equation
Jian Huang
Zhongdi Cen
Aimin Xu
Li-Bin Liu
Numerical Algorithms, 2020, 83 : 549 - 563
[45] A posteriori error estimation for a singularly perturbed Volterra integro-differential equation
Huang, Jian
Cen, Zhongdi
Xu, Aimin
Liu, Li-Bin
NUMERICAL ALGORITHMS, 2020, 83 (02) : 549 - 563
[46] UNIFORM CONVERGENCE RESULTS FOR SINGULARLY PERTURBED FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
Amiraliyev, Gabil M.
Durmaz, Muhammet Enes
Kudu, Mustafa
JOURNAL OF MATHEMATICAL ANALYSIS, 2018, 9 (06): : 55 - 64
[47] A Robust Numerical Method for the Singularly Perturbed Integro-Differential Equations
Arslan, Derya
Celik, Ercan
GAZI UNIVERSITY JOURNAL OF SCIENCE, 2025, 38 (01): : 267 - 273
[48] Singularly perturbed integro-differential equations with diagonal degeneration of the kernel in reverse time
Bobodzhanov, AA
Safonov, VF
DIFFERENTIAL EQUATIONS, 2004, 40 (01) : 120 - 127
[49] Singularly Perturbed Integro-Differential Equations with Diagonal Degeneration of the Kernel in Reverse Time
A. A. Bobodzhanov
V. F. Safonov
Differential Equations, 2004, 40 : 120 - 127
[50] An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
Durmaz, Muhammet Enes
Amirali, Ilhame
Amiraliyev, Gabil M.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (01) : 505 - 528

← 1 2 3 4 5 →