广义improved KdV方程的守恒差分格式

J4 ›› 2011, Vol. 46 ›› Issue (8): 4-7.

广义improved KdV方程的守恒差分格式

张天德¹,左进明²,段伶计¹

1.山东大学数学学院, 山东济南 250100; 2.山东理工大学理学院, 山东淄博 255049

收稿日期:2010-03-12 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:张天德(1962), 男, 教授, 主要从事偏微分方程数值解的研究. Email:zhangtd@sdu.edu.cn
基金资助:
山东省自然科学基金资助项目(Y2006A07)

Conservative scheme for the general improved KdV equation

ZHANG Tian-de¹, ZUO Jin-ming², DUAN Ling-ji¹

1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
2. School of Science, Shandong University of Technology, Zibo 255049, Shandong, China

Received:2010-03-12 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

对广义improved KdV (GIKdV)方程的初边值问题提出了一种守恒的隐式差分格式,利用能量分析方法证明了差分格式的稳定性和二阶收敛性,数值试验显示该格式是十分有效的。

关键词: 广义improved KdV (GIKdV)方程;差分格式;守恒性;收敛性;稳定性

Abstract:

A new conservative finite difference scheme is presented for an initial-boundary value problem of the general improved KdV(GIKdV) equation. It is proved by the discrete energy method that the scheme is unconditionally stable and second-order convergent. Numerical experiments demonstrate that the scheme is accurate efficient.

Key words: GIKdV equation; dfifference scheme; conservation; convergence; stability

张天德1,左进明2,段伶计1. 广义improved KdV方程的守恒差分格式[J]. J4, 2011, 46(8): 4-7.

ZHANG Tian-de1, ZUO Jin-ming2, DUAN Ling-ji1. Conservative scheme for the general improved KdV equation[J]. J4, 2011, 46(8): 4-7.

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