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| SRLW方程的多辛格式及其守恒律 | |
| 引用本文： | 孔令华,曾文平,刘儒勋,孔令健.SRLW方程的多辛格式及其守恒律[J].中国科学技术大学学报,2005,35(6):770-776. |
| 作者姓名： | 孔令华 曾文平 刘儒勋 孔令健 |
| 作者单位： | 1. 中国科学技术大学数学系,安徽,合肥,230026 2. 华侨大学数学系,福建,泉州,360021 3. 博达公路有限公司,江西,赣州,341000 |
| 基金项目： | 中国科学院资助项目，中国科技大学校科研和教改项目，北京市计算物理研究所科研项目，国务院侨务办公室科研项目，国家重点实验室基金 |
| 摘 要： | 考虑了对称正则长波方程(SRLW方程)的多辛算法.通过对SRLW方程作正则变换,得到了它的正则方程组及其几个守恒律.用多辛Euler方法离散此方程组得到了它的多辛格式,并且推导了它的局部能量守恒律的离散误差.消去多辛Euler格式的中间变量,得到了多辛Preissman格式.数值实验验证了所构造的格式的有效性扣长时间的数值稳定性,它能很好地模拟原孤立波,能量精度也较高. |
| 关 键 词： | 多辛格式 SRLW方程 守恒律 |
| 文章编号： | 0253-2778（2005）06-0770-07 |
| 收稿时间： | 2004-09-21 |
| 修稿时间： | 2005-01-12 |
Multi-symplectic Scheme of SRLW Equation and Conservation Laws |
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| KONG Ling-hua,ZENG Wen-ping,LIU Ru-xun,KONG Ling-jian.Multi-symplectic Scheme of SRLW Equation and Conservation Laws[J].Journal of University of Science and Technology of China,2005,35(6):770-776. | |
| Authors: | KONG Ling-hua ZENG Wen-ping LIU Ru-xun KONG Ling-jian |
| Institution: | 1. Dept. of Math. , University of Science and Technology of China, He f ei 230026,China; 2. Dept. of Math. , Huaqiao Univ. , Quanzhou 360021, China ; 3. Boda Highzoay Ltd. , Jiangxi 341000, China |
| Abstract: | We consider a multi-symplectic scheme for the SRLW equation in the paper. Canonical equations for the SRLW equation are presented which possess some conservation laws by canonical transformations. We show a multi-symplectic scheme for the equations by the multi-symplectic Euler method. The truncation error of its local discrete energy conservation law is also exhibited. A single variable multi-symplectic Preissman scheme is obtained by eliminating its mid-variables. Experiments show that the constructed scheme is valid and can preserve the original wave shape. They also verify that multi-symplectic schemes have long-term behavior as well as high energy accuracy. |
| Keywords: | multi-symplectic scheme SRLW equation conservation law |
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