色散方程的一类具任意稳定性的显格式

计算物理 ›› 1994, Vol. 11 ›› Issue (1): 85-90.

色散方程的一类具任意稳定性的显格式

张大凯

贵州大学数学系, 贵阳 550025

收稿日期:1992-07-02 修回日期:1993-04-26 出版日期:1994-03-25 发布日期:1994-03-25

A KIND OF EXPLICIT SCHEME WITH ARBITRARY STABILITY CONDITION FOR DISPERSION EQUATION

Zhang Dakai

Department of Mathematics, Guizhou Universily, Guiyang, 550025

Received:1992-07-02 Revised:1993-04-26 Online:1994-03-25 Published:1994-03-25

摘要/Abstract

摘要： 本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。

关键词: 色散方程, 双参数显式校正格式, 任意稳定性

Abstract: A kind of three level explicit difference scheme with two parameters m and θ,including four knots in the middle level is presented, for the dispersion equation u_r=au_xxx.When the m and θ satisfy a certain ralation, the stability condition is |γ|≤(m+1)/(4(m-1))(|m|>1).Thus, as m goes sufficiently neer to 1, an arbitrary stability condition can be obtained, and the order of the truncation error is not changed. The numerical example verifies the results of the theoretical analysis.

Key words: dispersion equation, explicit correction scheme with two parameters, arbitrary stability

张大凯. 色散方程的一类具任意稳定性的显格式[J]. 计算物理, 1994, 11(1): 85-90.

Zhang Dakai. A KIND OF EXPLICIT SCHEME WITH ARBITRARY STABILITY CONDITION FOR DISPERSION EQUATION[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 11(1): 85-90.

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