A fourth-order AVF method for the numerical integration of sine-Gordon equation

被引：32

作者：

Jiang, Chaolong ^{[1
,2
]}

Sun, Jianqiang ^{[2
]}

Li, Haochen ^{[3
,4
]}

Wang, Yifan ^{[2
]}

机构：

[1] Nanjing Normal Univ, Sch Math & Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China

[2] Hainan Univ, Coll Informat Sci & Technol, Dept Math, Haikou 570228, Hainan, Peoples R China

[3] Peking Univ, CAPT, LMAM, Beijing 100871, Peoples R China

[4] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 313卷

基金：

美国国家科学基金会;

关键词：

Energy-preserving; Average vector field method; Pseudo-spectral method; Sine-Gordon equation; Soliton; BACKWARD ERROR ANALYSIS; SYMPLECTIC RUNGE-KUTTA; ALGORITHMS; COLLOCATION; SCHEMES;

D O I：

10.1016/j.amc.2017.05.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new scheme, which has energy-preserving property, is proposed for solving the sine-Gordon equation with periodic boundary conditions. It is obtained by the Fourier pseudo-spectral method and the fourth order average vector field method. In numerical experiments, the new high order energy-preserving scheme is compared with a number of existing numerical schemes for the one dimensional sine-Gordon equation. The new high order energy-preserving scheme for the two dimensional sine-Gordon equation is also investigated. Numerical results are addressed to further illustrate the conservation of energy and the evolutional behaviors of solitons. (C) 2017 Published by Elsevier Inc.

引用

页码：144 / 158

页数：15

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