Landau-Ginzburg-Higgs方程的多辛Runge-Kutta方法  

Multi-Symplectic Runge-Kutta Methods for Landau-Ginzburg-Higgs Equation

作　　者：胡伟鹏[1,2] 邓子辰[1,3] 韩松梅[1] 范玮[2] 

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072 [2]西北工业大学动力与能源学院,西安710072 [3]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《应用数学和力学》2009年第8期963-969,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10772147;10632030);教育部博士点基金资助项目(20070699028);陕西省自然科学基金资助项目(2006A07);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目(GZ0802)

摘　　要：非线性波动方程作为一类重要的数学物理方程吸引着众多的研究者,基于Hamilton空间体系的多辛理论研究了Landau-Ginzburg-Higgs方程的多辛算法,讨论了利用Runge-Kutta方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律、局部能量守恒律和局部动量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.The nonlinear wave equation, describing many important physical phenomena,has been investigated widely in last several decades. Landau-Ginzburg-Higgs equation, a typical nonlinear wave e- quation, was sdudied based on the multi-symplectic theory in Hamilton space. The multi-symplectic Runge-Kutta method was reviewed and a semi-implicit scheme with certain discrete conservation laws was constructed to solve the first-order partial differential equations that were derived from the Lan- dau-Ginzburg-Higgs equation. The results of numerical experiment for soliton solution of the Landau- Ginzburg-Higgs equation were reported finally, which show that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.

关 键 词：多辛 Landau-Ginzburg-Higgs方程 Runge—Kutta方法 守恒律 孤子解 

分 类 号：O175.24[理学—数学]