正则长波方程的新的守恒差分方法

A New Conservative Finite Difference Method for Regularized Long Wave Equation

对正则长波方程进行处理得到一个"耗散项"h^2/12u_■,提出了一个新的守恒的三层差分格式,分析了格式的稳定性与收敛性,截断误差为 O(τ~2+h^2)。并通过数值例子与已有的格式,C-N 格式进行了比较。数值结果表明,本文格式不仅保持了计算量小的特点,而且数值精度有着显著的提高。

In this paper, a new conservative finite difference scheme for initial value and boundary value problem of regularized long--wave （RLW） equation is considered, whose truncation error is . We deal with RLW equation and acquire a so--called dispersive term. Then we introduce a parameter to the scheme. The dispersive term is a new characteristic of the scheme. And its convergence and stability are proved. A numerical example shows that the method has small amount of computation and higher precision than the other schemes.