Journal
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
Volume 35, Issue 3, Pages 369-380Publisher
SHANGHAI UNIV
DOI: 10.1007/s10483-014-1797-6
Keywords
nonlinear wave equation; multi-symplectic method; backward error analysis
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Funding
- National Natural Science Foundation of China [11161017, 11071251, 10871099]
- National Basic Research Program of China (973 Program) [2007CB209603]
- Natural Science Foundation of Hainan Province [110002]
- Scientific Research Foundation of Hainan University [kyqd1053]
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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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