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
收藏
页码：214 / 223
页数：10
相关论文
共 50 条
  • [31] Singularly Perturbed Multidimensional Parabolic Equation with Rapidly Oscillating Free Term
    A. S. Omuraliev
    E. Abylaeva
    Ukrainian Mathematical Journal, 2022, 73 : 1906 - 1917
  • [32] Singularly Perturbed Multidimensional Parabolic Equation with Rapidly Oscillating Free Term
    Omuraliev, A. S.
    Abylaeva, E.
    UKRAINIAN MATHEMATICAL JOURNAL, 2022, 73 (12) : 1906 - 1917
  • [33] Singularly perturbed integro-differential equations with degenerate Hammerstein's kernel
    Bobodzhanova, M. A.
    Kalimbetov, B. T.
    Safonov, V. F.
    BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS SERIES, 2024, 116 (04): : 57 - 68
  • [34] Regularization method for nonlinear integro-differential systems of Fredholm type with rapidly varying kernels
    Bobodzhanov, A. A.
    Safonov, V. F.
    DIFFERENTIAL EQUATIONS, 2015, 51 (02) : 255 - 267
  • [35] Regularization method for nonlinear integro-differential systems of Fredholm type with rapidly varying kernels
    A. A. Bobodzhanov
    V. F. Safonov
    Differential Equations, 2015, 51 : 255 - 267
  • [36] An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation
    Durmaz, Muhammet Enes
    Yapman, Omer
    Kudu, Mustafa
    Amiraliyev, Gabil M.
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2023, 52 (02): : 326 - 339
  • [37] Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation
    Amiraliyev, Gabil M.
    Durmaz, Muhammet Enes
    Kudu, Mustafa
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2020, 27 (01) : 71 - 88
  • [38] Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating co-sine
    Bobodzhanov, Abdukhafiz
    Kalimbetov, Burkhan
    Pardaeva, Nilufar
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2024, 32 (01): : 74 - 85
  • [39] The asymptotic method of differential inequalities for singularly perturbed integro-differential equations
    N. N. Nefedov
    A. G. Nikitin
    Differential Equations, 2000, 36 : 1544 - 1550
  • [40] The coupled method for singularly perturbed Volterra integro-differential equations
    Xia Tao
    Yinghui Zhang
    Advances in Difference Equations, 2019
12345