Klein-Gordon-Zakharov 方程的一类初边值问题的数值解

数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 494-504.

Klein-Gordon-Zakharov 方程的一类初边值问题的数值解

(1. 常熟理工学院数学系江苏常熟 215500; 2. 南京航空航天大学数学系南京 210016)

收稿日期:2007-10-08 修回日期:2008-11-30 出版日期:2009-04-25 发布日期:2009-04-25
基金资助:
国家自然科学基金(10471023)资助

Numerical Approximation of Solution for the Initial-boundary Value Problem of the Klein-Gordon-Zakharov Equations

(1. Department of Mathematics, Changshu Institute of Technology, Jiangsu Changshu 215500; 2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016)

Received:2007-10-08 Revised:2008-11-30 Online:2009-04-25 Published:2009-04-25
Supported by:
国家自然科学基金(10471023)资助

摘要/Abstract

摘要：

对Klein-Gordon-Zakharov方程的一类初边值问题提出了一个含参数θ 的守恒型差分格式, 并且在先验估计的基础上, 利用能量方法证明了差分解的收敛性且收敛阶为O(h²+τ²).数值实验结果表明此格式是精确有效的.

关键词: KGZ方程, 守恒差分格式, 先验估计, 收敛性

Abstract:

In this work, a conservative difference scheme with a parameter $\theta$ is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov equations. On the basis of a priori estimates, convergence of the difference solutions is proved with order O(h²+τ²) in the energy norm. Numerical experiments emonstrate the accuracy and effectiveness of the proposed scheme.

Key words: KGZ equations, Conservative difference scheme, Priori estimates, Convergence

中图分类号:

65M06

陈娟; 张鲁明. Klein-Gordon-Zakharov 方程的一类初边值问题的数值解[J]. 数学物理学报, 2009, 29(2): 494-504.

Chen Juan; Zhang Luming. Numerical Approximation of Solution for the Initial-boundary Value Problem of the Klein-Gordon-Zakharov Equations[J]. Acta mathematica scientia,Series A, 2009, 29(2): 494-504.

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