若干高精度恒稳的半显式差分格式

计算物理 ›› 1992, Vol. 9 ›› Issue (4): 443-444.

若干高精度恒稳的半显式差分格式

曾文平, 王子丁

华侨大学应用数学系, 泉州 362011

收稿日期:1992-02-11 出版日期:1992-12-25 发布日期:1992-12-25
基金资助:
国家教委留学生基金

A CERTAIN NUMBER OF ABSOLUTELY STABLE AND HIGH ACCURACY OF SEMI-EXDLICIT DIFFERENCE SCHEMES

Zeng Wenping, Wang Ziding

Overseas Chinese University, 362011

Received:1992-02-11 Online:1992-12-25 Published:1992-12-25

摘要/Abstract

摘要： 本文构造了解色散方程u₁=au_xxx的若干三层恒稳的半显式差分格式。第Ⅰ、Ⅱ类格式的局部截断误差的阶为O(τ²+h²+(τ²)/(h³));而第Ⅲ、Ⅳ类格式的局部截断误差的阶为O(τ²+h⁴+((τ)/(h))²+τh)。用判别稳定性的Von Neumann准则可证明:第Ⅰ、Ⅱ类格式及当参数α≤1时的第Ⅲ、Ⅳ类格式都是无条件稳定的,并且当必须的边界条件给定时它们可以显式地进行计算。

关键词: 半显式差分格式, 无条件稳定, 色散方程

Abstract: In this paper, Four classes of three level semi-explieit difference Schemes for solving the dispersive equation u₁=au_xxx are developed. The orders of the local truncation error are all O(τ²+h²+(τ²)/(h³)) or O(τ²+h⁴+((τ)/(h))²+τh). The schemes of Ⅰ,Ⅱ and when paramater α≤1, the schemes of Ⅲ. Ⅳ are all shown to be unconditionally stable by the Von Neumann criterion for stability. And thev can be calculated explicitly when necessary boundary value are given.

Key words: semi-explicit difference scheme, unconditional stability dispersive equation

曾文平, 王子丁. 若干高精度恒稳的半显式差分格式[J]. 计算物理, 1992, 9(4): 443-444.

Zeng Wenping, Wang Ziding. A CERTAIN NUMBER OF ABSOLUTELY STABLE AND HIGH ACCURACY OF SEMI-EXDLICIT DIFFERENCE SCHEMES[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 9(4): 443-444.

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