New explicit multi-symplectic scheme for nonlinear wave equation

作     者：李昊辰 孙建强 秦孟兆 

作者机构：Department of MathematicsCollege of Information Science and TechnologyHainan University State Key Laboratory of Scientific and Engineering ComputingAcademy of Mathematics and System SciencesChinese Academy of Sciences 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2014年第35卷第3期

页      面：369-380页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11161017,11071251,and 10871099) the National Basic Research Program of China(973 Program)(No.2007CB209603) the Natural Science Foundation of Hainan Province(No.110002) the Scientific Research Foun-dation of Hainan University(No.kyqd1053) 

主　　题：nonlinear wave equation multi-symplectic method backward error analysis 

摘      要：Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.