Finite difference scheme for one nonlinear parabolic integro-differential equation

被引：1
|
作者：
Jangveladze, Temur
Kiguradze, Zurab [1 ]
机构：
[1] Tbilisi State Univ, Ilia Vekua Inst Appl Math Ivane Javakhishvili, 2 Univ St, GE-0186 Tbilisi, Georgia
来源：
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2016年 / 170卷 / 03期
关键词：
Nonlinear parabolic integro-differential equation; Initial-boundary value problem; Mixed boundary conditions; Finite difference scheme; Convergence;
D O I：
10.1016/j.trmi.2016.09.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Initial-boundary value problem with mixed boundary conditions for one nonlinear parabolic integro-differential equation is considered. The model is based on Maxwell system describing the process of the penetration of a electromagnetic field into a substance. Unique solvability and asymptotic behavior of solution are fixed. Main attention is paid to the convergence of the finite difference scheme. More wide cases of nonlinearity that already were studied are investigated. (C) 2016 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.
引用
收藏
页码：395 / 401
页数：7
相关论文
共 50 条
  • [1] Finite difference scheme for one system of nonlinear partial integro-differential equations
    Hecht, Frederic
    Jangveladze, Temur
    Kiguradze, Zurab
    Pironneau, Olivier
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2018, 328 : 287 - 300
  • [2] Large time behavior of solutions and finite difference scheme to a nonlinear integro-differential equation
    Jangveladze, Temur
    Kiguradze, Zurab
    Neta, Beny
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 57 (05) : 799 - 811
  • [3] A finite difference scheme for the nonlinear time-fractional partial integro-differential equation
    Guo, Jing
    Xu, Da
    Qiu, Wenlin
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3392 - 3412
  • [4] A predictor-corrector compact finite difference scheme for a nonlinear partial integro-differential equation
    Hu, Shufang
    Qiu, Wenlin
    Chen, Hongbin
    [J]. INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2022, 23 (3-4) : 553 - 563
  • [5] Finite Difference Scheme to a Nonlinear Integro-Differential Equation Associated with the Penetration of a Magnetic Field into a Substance
    Jangveladze, Temur
    Kiguradze, Zurab
    [J]. PROCEEDINGS OF THE WSEAS INTERNATIONAL CONFERENCE ON FINITE DIFFERENCES, FINITE ELEMENTS, FINITE VOLUMES, BOUNDARY ELEMENTS, 2009, : 186 - +
  • [6] Finite element method for a nonlinear parabolic integro-differential equation in higher spatial dimensions
    Sharma, Nisha
    Sharma, Kapil K.
    [J]. APPLIED MATHEMATICAL MODELLING, 2015, 39 (23-24) : 7338 - 7350
  • [7] DIFFERENCE DERIVATIVE FOR AN INTEGRO-DIFFERENTIAL NONLINEAR VOLTERRA EQUATION
    Guebbai, H.
    Lemita, S.
    Segni, S.
    Merchela, W.
    [J]. VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2020, 30 (02): : 176 - 188
  • [8] Finite difference approximation of a nonlinear integro-differential system
    Jangveladze, Temur
    Kiguradze, Zurab
    Neta, Beny
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (02) : 615 - 628
  • [9] A second order finite difference scheme for singularly perturbed Volterra integro-differential equation
    Mbroh, Nana Adjoah
    Noutchie, Suares Clovis Oukouomi
    Massoukou, Rodrigue Yves M'pika
    [J]. ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (04) : 2441 - 2447
  • [10] Finite central difference/finite element approximations for parabolic integro-differential equations
    Li, Wulan
    Da, Xu
    [J]. COMPUTING, 2010, 90 (3-4) : 89 - 111
12345