Petrov-Galerkin有限元法求正则化长波方程的数值解

HUMERICAL SOLUTION OF THE REGULARSZEB LOG-WAVE EQUATION BY PETROV-GALERKIN FINITE EIEMENT METHOB

本文给出数值求解正则化长波方程(简称为KLW方程)初值问题的一种Petrov-Galerkin有限无法。由于它对时间和空间变量分别有二阶和四阶精度,所以对一个孤立波的进波解,数值结果与精确解极为吻合。对于两个孤立波的相互碰撞,则发现碰撞后有微小振荡尾波存在,从而严格说来。

A numerical solution of the initial value problem of regularized long-Wave equation (RLW Equation) was made by a Petrov-Galerkin finite elemnte method. The numerical resuts are consistent with the exact solution of propagation of single solitary wave, due to second-order and fourth-order accuracy for the time and spacing variable respectively. For the collision of two soli-tons, there is a slight oscilatoiy wave trail after their collision, so it doesn't have the quality of soliton strictly.