The analysis of operator splitting for the Gardner equation

被引：2
|
作者：
Zhao, Jingjun [1 ]
Zhan, Rui [1 ]
Xu, Yang [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2019年 / 144卷
基金：
中国国家自然科学基金;
关键词：
Operator splitting; Strang splitting; Convergence; Gardner equation; DE-VRIES EQUATION; NUMERICAL-SOLUTION; WAVE-PROPAGATION; KORTEWEG; POSEDNESS; SCHEMES;
D O I：
10.1016/j.apnum.2019.04.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the convergence property of the Strang splitting for the Gardner equation. We assume that the Gardner equation is locally well-posed and the solution is bounded. We first obtain the regularity properties of the nonlinear divided equation. With these regularity properties, the Strang splitting is proved to converge at the expected rate in L-2. Numerical experiments demonstrate the theoretical result and serve to compare the accuracy and efficiency of different time stepping methods. Finally, the proposed method is applied to simulate the multi solitons collisions for the Gardner equation. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：151 / 175
页数：25
相关论文
共 50 条
  • [41] A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation
    Alexandre CABOUSSAT
    Roland GLOWINSKI
    Chinese Annals of Mathematics(Series B), 2015, 36 (05) : 659 - 688
  • [42] A penalty-regularization-operator splitting method for the numerical solution of a scalar Eikonal equation
    Alexandre Caboussat
    Roland Glowinski
    Chinese Annals of Mathematics, Series B, 2015, 36 : 659 - 688
  • [43] Operator splitting for numerical solution of the modified Burgers' equation using finite element method
    Ucar, Yusuf
    Yagmurlu, Nuri M.
    Celikkaya, Ihsan
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (02) : 478 - 492
  • [44] FPTU recurrence within the Gardner equation
    Flamarion, Marcelo V.
    Pelinovsky, Efim
    NONLINEAR DYNAMICS, 2024,
  • [45] On the ill-posedness of the Gardner equation
    Alejo, Miguel A.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 396 (01) : 256 - 260
  • [46] Bilinear approach to the supersymmetric Gardner equation
    Babalic, C. N.
    Carstea, A. S.
    THEORETICAL AND MATHEMATICAL PHYSICS, 2016, 188 (02) : 1172 - 1180
  • [47] New solutions of the Gardner equation: Analytical and numerical analysis of its dynamical understanding
    Betchewe, Gambo
    Victor, Kuetche Kamgang
    Thomas, Bouetou Bouetou
    Crepin, Kofane Timoleon
    APPLIED MATHEMATICS AND COMPUTATION, 2013, 223 : 377 - 388
  • [48] PARAREAL OPERATOR SPLITTING TECHNIQUES FOR MULTI-SCALE REACTION WAVES: NUMERICAL ANALYSIS AND STRATEGIES
    Duarte, Max
    Massot, Marc
    Descombes, Stephane
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2011, 45 (05): : 825 - 852
  • [49] STRANG SPLITTING METHODS FOR A QUASILINEAR SCHRODINGER EQUATION: CONVERGENCE, INSTABILITY, AND DYNAMICS
    Lu, Jianfeng
    Marzuola, Jeremy L.
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (05) : 1051 - 1074
  • [50] Preconditioning a class of fourth order problems by operator splitting
    Baensch, Eberhard
    Morin, Pedro
    Nochetto, Ricardo H.
    NUMERISCHE MATHEMATIK, 2011, 118 (02) : 197 - 228
12345