五阶色散KdV方程的交替分段显-隐差分格式

J4 ›› 2010, Vol. 45 ›› Issue (10): 116-121.

五阶色散KdV方程的交替分段显-隐差分格式

左进明1,张天德2

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

收稿日期:2009-04-01 出版日期:2010-10-16 发布日期:2010-10-19
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资助项目(Y2006A07)

Alternating segment explicit-implicit scheme for the fifth-order dispersive KdV equation

ZUO Jin-ming1, ZHANG Tian-de2

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

Received:2009-04-01 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

对五阶色散KdV方程给出了一组非对称的差分格式,用这些差分格式与显、隐差分格式组合,构造了一类具有本性并行的交替分段显-隐格式，证明了格式的线性绝对稳定性。数值试验表明,这种方法有很好的精度。

关键词: 五阶色散KdV方程; 并行计算; 交替分段显-隐差分格式; 线性绝对稳定

Abstract:

A group of asymmetric difference schemes to approach the fifth-order dispersive KdV equation are given. Using the schemes and the full explicit difference scheme and the full implicit difference scheme, the alternating difference scheme for solving the fifthorder dispersive KdV equation is constructed. The scheme is linear unconditionally stable by analysis of linearization procedure, and is used directly on the parallel computer. Numerical experiments show that the method has high accuracy.

Key words: the fifth-order dispersive KdV equation; parallel computation; alternating segment explicitimplicit scheme; linear unconditionally stable

左进明1,张天德2. 五阶色散KdV方程的交替分段显-隐差分格式[J]. J4, 2010, 45(10): 116-121.

ZUO Jin-ming1, ZHANG Tian-de2. Alternating segment explicit-implicit scheme for the fifth-order dispersive KdV equation[J]. J4, 2010, 45(10): 116-121.

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