| New explicit multi-symplectic scheme for nonlinear wave equation简 |
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| 引用本文： | 李昊辰,孙建强,秦孟兆.New explicit multi-symplectic scheme for nonlinear wave equation简[J].应用数学和力学(英文版),2014,35(3):369-380. |
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| 作者姓名： | 李昊辰 孙建强 秦孟兆 |
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| 基金项目： | 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) |
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| 摘 要： |
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New explicit multi-symplectic scheme for nonlinear wave equation |
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| Hao-chen Li,Jian-qiang Sun,Meng-zhao Qin.New explicit multi-symplectic scheme for nonlinear wave equation[J].Applied Mathematics and Mechanics(English Edition),2014,35(3):369-380. |
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| Authors: | Hao-chen Li Jian-qiang Sun Meng-zhao Qin |
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| Institution: | 1. Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, Hainan Province, P. R. China
2. State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, P. R. China
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| Abstract: | 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. |
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| Keywords: | nonlinear wave equation multi-symplectic method backward error analysis |
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