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

[31] On the numerical solution to a nonlinear wave equation associated with the first painlevé equation: an operator-splitting approach
Roland Glowinski
Annalisa Quaini
Chinese Annals of Mathematics, Series B, 2013, 34 : 237 - 254
[32] Numerical approximation of the conservative Allen-Cahn equation by operator splitting method
Weng, Zhifeng
Zhuang, Qingqu
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (12) : 4462 - 4480
[33] Operator splitting and commutativity analysis in the Danish Eulerian Model
Dimov, I
Faragó, I
Havasi, A
Zlatev, Z
MATHEMATICS AND COMPUTERS IN SIMULATION, 2004, 67 (03) : 217 - 233
[34] Bright and dark rogue internal waves: The Gardner equation approach
Bokaeeyan, Mahyar
Ankiewicz, A.
Akhmediev, N.
PHYSICAL REVIEW E, 2019, 99 (06)
[35] Dynamical analysis of diverse exact solutions, soliton surfaces and continuum limit theory for a semidiscrete Gardner equation
Wei, Meng-Chu
Wen, Xiao-Yong
Zhou, Jian-Chen
NONLINEAR DYNAMICS, 2025, 113 (06) : 5671 - 5689
[36] A SURVEY ON OPERATOR SPLITTING AND DECOMPOSITION OF CONVEX PROGRAMS
Lenoir, Arnaud
Mahey, Philippe
RAIRO-OPERATIONS RESEARCH, 2017, 51 (01) : 17 - 41
[37] High order operator splitting methods based on an integral deferred correction framework
Christlieb, Andrew J.
Liu, Yuan
Xu, Zhengfu
JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 294 : 224 - 242
[38] Non-iterative compact operator splitting scheme for Allen-Cahn equation
Lee, Seunggyu
COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (07)
[39] An Efficient WLP-Based Method with Operator Splitting Technique for Solving Wave Equation
Li, Jie
Tang, Min
Mao, Junfa
2023 53RD EUROPEAN MICROWAVE CONFERENCE, EUMC, 2023, : 540 - 543
[40] A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation
Caboussat, Alexandre
Glowinski, Roland
CHINESE ANNALS OF MATHEMATICS SERIES B, 2015, 36 (05) : 659 - 688

← 1 2 3 4 5 →