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

页码：151 / 175

页数：25

共 50 条

[11] On the Operator Splitting and Integral Equation Preconditioned Deferred Correction Methods for the "Good" Boussinesq Equation
Zhang, Cheng
Huang, Jingfang
Wang, Cheng
Yue, Xingye
JOURNAL OF SCIENTIFIC COMPUTING, 2018, 75 (02) : 687 - 712
[12] THE GARDNER EQUATION IN ELASTODYNAMICS
Coclite, G. M.
Maddalena, F.
Puglisi, G.
Romano, M.
Saccomandi, G.
SIAM JOURNAL ON APPLIED MATHEMATICS, 2021, 81 (06) : 2346 - 2361
[13] A fast solvable operator-splitting scheme for time-dependent advection diffusion equation
Chen, Chengyu
Lin, Xue-Lei
APPLIED NUMERICAL MATHEMATICS, 2024, 204 : 48 - 59
[14] Operator Splitting Method to Solve the Linear Complementarity Problem for Pricing American Option: An Approximation of Error
Yadav, Deepak Kumar
Bhardwaj, Akanksha
Kumar, Alpesh
COMPUTATIONAL ECONOMICS, 2024, 64 (06) : 3353 - 3379
[15] A second order operator splitting numerical scheme for the "good" Boussinesq equation
Zhang, Cheng
Wang, Hui
Huang, Jingfang
Wang, Cheng
Yue, Xingye
APPLIED NUMERICAL MATHEMATICS, 2017, 119 : 179 - 193
[16] Operator splitting for the neutron transport equation in two-dimensional geometry
Akesbi, S
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (06): : 1109 - 1122
[17] An analysis of operator splitting techniques in the stiff case
Sportisse, B
JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 161 (01) : 140 - 168
[18] AN OPERATOR SPLITTING SCHEME FOR THE FRACTIONAL KINETIC FOKKER-PLANCK EQUATION
Duong, Manh Hong
Lu, Yulong
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (10) : 5707 - 5727
[19] An a posteriori - A priori analysis of multiscale operator splitting
Estep, D.
Ginting, V.
Ropp, D.
Shadid, J. N.
Tavener, S.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (03) : 1116 - 1146
[20] Efficient operator splitting and spectral methods for the time-space fractional Black-Scholes equation
Almushaira, Mustafa
Chen, Feng
Liu, Fei
RESULTS IN APPLIED MATHEMATICS, 2021, 10

← 1 2 3 4 5 →