变系数广义正则长波方程的一种线性差分格式

J4 ›› 2011, Vol. 46 ›› Issue (12): 23-28.

变系数广义正则长波方程的一种线性差分格式

马维元,马刚

西北民族大学数学与计算机科学学院, 甘肃兰州 730030

收稿日期:2010-11-29 出版日期:2011-12-20 发布日期:2011-12-24
作者简介:马维元(1980- ),男,硕士,讲师,研究方向为微分方程数值解法. Email:mwy2004@126.com
基金资助:
西北民族大学中央高校基本科研业务费专项资金资助项目(ZYZ2011082)

A linearized finite difference scheme for the generalized regularized long-wave equation with a variable coefficient

MA Wei-yuan, MA Gang

School of Mathematics and Computer Science, Lanzhou 730030, Gansu, China

Received:2010-11-29 Online:2011-12-20 Published:2011-12-24

摘要/Abstract

摘要：

对变系数阻尼广义正则长波方程给出了一种线性差分格式,通过 Brouwer 不动点定理证明了差分格式解的存在性,并得到了差分解的收敛性与稳定性。数值试验表明该格式是有效、可靠的。

关键词: DGRLW方程;有限差分格式;存在性;收敛性;稳定性

Abstract:

A linearized finite difference scheme for the damped generalized regularized long-wave equation with a variable coefficient is presented. The existence of the difference scheme is shown by Brouwer fixed-point theorem. Convergence and stability of difference solution are proved. Numerical experiment results demonstrate that the scheme is effective and reliable.

Key words: DGRLW equation; finite difference scheme; existence; convergence; stability

马维元,马刚. 变系数广义正则长波方程的一种线性差分格式[J]. J4, 2011, 46(12): 23-28.

MA Wei-yuan, MA Gang. A linearized finite difference scheme for the generalized regularized long-wave equation with a variable coefficient[J]. J4, 2011, 46(12): 23-28.

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