New explicit multi-symplectic scheme for nonlinear wave equation  

作　　者：李昊辰 孙建强 秦孟兆 

机构地区：[1]Department of Mathematics,College of Information Science and Technology,Hainan University [2]State Key Laboratory of Scientific and Engineering Computing,Academy of Mathematics and System Sciences,Chinese Academy of Sciences

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第3期369-380,共12页应用数学和力学（英文版）

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)

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.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.

关 键 词：nonlinear wave equation multi-symplectic method backward error analysis 

分 类 号：O411.1[理学—理论物理]