Error analysis of waveform relaxation method for semi-linear partial differential equations

被引：4
|
作者：
Ladics, Tamas [1 ]
机构：
[1] Szent Istvan Univ, Ybl Miklos Coll Bldg, H-1146 Budapest, Hungary
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 285卷
基金：
美国国家科学基金会;
关键词：
Semi-linear partial differential equations; Waveform relaxation; Numerical solutions; Convergence; Windowing technique; DYNAMIC ITERATION;
D O I：
10.1016/j.cam.2015.02.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The waveform relaxation (WR) method is investigated for semi-linear partial differential equations. Explicit error estimation is given for the iteration error. A way to combine WR with convergent numerical methods is proposed, the error of the combined method is analyzed and its convergence is proven. The effect of the application of time windows is discussed. Numerical tests are presented to confirm the theoretical results. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：15 / 31
页数：17
相关论文
共 50 条
  • [1] A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations
    Liu, Jun
    Jiang, Yao-Lin
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (17) : 4245 - 4263
  • [2] A NOTE ON FIRST ORDER SEMI-LINEAR PARTIAL DIFFERENTIAL EQUATIONS
    KOLODNER, II
    PEDERSON, RN
    AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (03): : 275 - &
  • [3] On semi-linear degenerate backward stochastic partial differential equations
    Ying Hu
    Jin Ma
    Jiongmin Yong
    Probability Theory and Related Fields, 2002, 123 : 381 - 411
  • [4] On semi-linear degenerate backward stochastic partial differential equations
    Hu, Y
    Ma, J
    Yong, JM
    PROBABILITY THEORY AND RELATED FIELDS, 2002, 123 (03) : 381 - 411
  • [5] A parareal approach of semi-linear parabolic equations based on general waveform relaxation
    Li, Jun
    Jiang, Yao-Lin
    Miao, Zhen
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (06) : 2017 - 2043
  • [6] Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations
    Descombes, Stephane
    Dolean, Victorita
    Gander, Martin J.
    DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XIX, 2011, 78 : 423 - +
  • [7] Probabilistic interpretation of a system of semi-linear parabolic partial differential equations
    Pardoux, E
    Pradeilles, F
    Rao, ZS
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 1997, 33 (04): : 467 - 490
  • [8] Existence, uniqueness and stability of semi-linear rough partial differential equations
    Friz, Peter K.
    Nilssen, Torstein
    Stannat, Wilhelm
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (04) : 1686 - 1721
  • [9] Waveform relaxation of partial differential equations
    Jiang, Yao-Lin
    Miao, Zhen
    NUMERICAL ALGORITHMS, 2018, 79 (04) : 1087 - 1106
  • [10] Waveform relaxation of partial differential equations
    Yao-Lin Jiang
    Zhen Miao
    Numerical Algorithms, 2018, 79 : 1087 - 1106
12345