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
收藏
页码：144 / 158
页数：15
相关论文
共 42 条
[1]   FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS [J].
ARGYRIS, J ;
HAASE, M ;
HEINRICH, JC .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1991, 86 (01) :1-26
[2]   Numerical solution of two-dimensional sine-Gordon and MBE models using Fourier spectral and high order explicit time stepping methods [J].
Asgari, Zohreh ;
Hosseini, S. M. .
COMPUTER PHYSICS COMMUNICATIONS, 2013, 184 (03) :565-572
[3]   A third order numerical scheme for the two-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2007, 76 (04) :271-282
[4]  
Bratsos A. G., 2008, J COMPUT APPL MATH, V85, P241
[5]  
Bratsos A. G., 2007, INT J COMPUT MATH, V206, P251
[6]   Numerical methods for Hamiltonian PDEs [J].
Bridges, Thomas J. ;
Reich, Sebastian .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (19) :5287-5320
[7]   Energy conservation issues in the numerical solution of the semilinear wave equation [J].
Brugnano, L. ;
Frasca Caccia, Gianluca ;
Iavernaro, F. .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 270 :842-870
[8]  
Brugnano L., 2010, JNAIAM J NUMER ANAL, V5, P17
[9]   Efficient implementation of Gauss collocation and Hamiltonian boundary value methods [J].
Brugnano, Luigi ;
Frasca Caccia, Gianluca ;
Iavernaro, Felice .
NUMERICAL ALGORITHMS, 2014, 65 (03) :633-650
[10]   A note on the efficient implementation of Hamiltonian BVMs [J].
Brugnano, Luigi ;
Iavernaro, Felice ;
Trigiante, Donato .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 236 (03) :375-383
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