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J4 ›› 2011, Vol. 46 ›› Issue (12): 19-22.

• 论文 • 上一篇    下一篇

广义Improved KdV方程的守恒线性隐式差分格式

左进明, 张耀明   

  1. 山东理工大学理学院, 山东 淄博 255049
  • 收稿日期:2010-10-27 出版日期:2011-12-20 发布日期:2011-12-24
  • 作者简介:左进明(1975- ), 男, 硕士, 主要从事偏微分方程数值解的研究. Email: zuojinming@sdut.edu.cn
  • 基金资助:

    山东省自然科学基金重点资助项目(ZR2010AZ003);国家自然科学基金资助项目(10571110)

Conservative linearimplicit scheme for the general Improved KdV equation

ZUO Jin-ming, ZHANG Yao-ming   

  1. School of Science, Shandong University of Technology, Zibo 255049, Shandong, China
  • Received:2010-10-27 Online:2011-12-20 Published:2011-12-24

摘要:

对广义Improved KdV (GIKdV)方程的初边值问题提出了一种守恒的线性隐式差分格式,并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有效的。

关键词: 广义Improved KdV (GIKdV)方程;线性隐式差分格式;守恒性;收敛性;稳定性

Abstract:

A new conservative linear-implicit 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 and efficient.

Key words: GIKdV equation; linear-implicit difference scheme; conservation; convergence; stability

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