几个非线性波动方程的数值方法  

Computational Methods for Some Non-linear Wave Equations

作　　者：张天德[1] 左进明[2] 鲁统超[1] 曹庆杰[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100 [2]山东理工大学数学与信息科学学院,淄博255049

出　　处：《工程数学学报》2006年第5期780-786,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471079);教育部高等学校博士点基金(20030422049)

摘　　要：文采用一种线性隐格式来解Korteweg-de Vries(KDV)/(GKDV)方程,对这种方法做一下推广,就能应用到Kadomtsev-Petviashvili(KP)方程以及它的广义形式(GKP)方程。这种方法是无条件稳定的,且是无损耗的。数值实验描述了一个线性孤波运动的情形以及两个孤波交互的情形,从结果来看,它们满足孤立子解的两个守恒-动量守恒和能量守恒。Computation methods based on a linearized implicit scheme are proposed for the solution of the Kadomtsev-petviashvili （Kp） equation and its generalized form （GKP）. The methods developed for the Kp equation are applied with minor modifications to the generalized case. An important advantage to be gained from the linearized implicit methods is unconditionally stable. Numerical results portraying a single line-soliton solution and the interaction of two-line solition are reported for the GKDV and GKP equation.

关 键 词：数值方法 KP/GKP方程 孤波 稳定性分析 

分 类 号：O241.82[理学—计算数学]