Multisymplectic five-point scheme for the nonlinear wave equation |
| |
Authors: | WANG Yushun WANG Bin Yang Hongwei WANG Yunfeng |
| |
Affiliation: | WANG Yushun~(1,2), WANG Bin~1, YANG Hongwei~1 & WANG Yunfeng~1 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029. China; 2. Permanent address: School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097. China |
| |
Abstract: | In this paper, we introduce the multisymplectic structure of the nonlinear wave equation, and prove that the classical five-point scheme for the equation is multisymplectic. Numerical simulations of this multisymplectic scheme on highly oscillatory waves of the nonlinear Klein-Gordon equation and the collisions between kink and anti-kink solitons of the sine-Gordon equation are also provided. The multisymplectic schemes do not need to discrete PDEs in the space first as the symplectic schemes do and preserve not only the geometric structure of the PDEs accurately, but also their first integrals approximately such as the energy, the momentum and so on. Thus the multisymplectic schemes have better numerical stability and long-time numerical behavior than the energy-conserving scheme and the symplectic scheme. |
| |
Keywords: | symplectic scheme energy-conserving scheme multisymplectic scheme nonlinear wave equation |
本文献已被 万方数据 等数据库收录! |
| 点击此处可从《科学通报(英文版)》浏览原始摘要信息 |
|
点击此处可从《科学通报(英文版)》下载全文 |
|