KuramotoSivashinsky方程的交替分组方法

J4 ›› 2011, Vol. 46 ›› Issue (12): 29-32.

KuramotoSivashinsky方程的交替分组方法

左进明¹,张耀明¹,张天德²,李娜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:2010-12-30 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, 研究方向为偏微分方程数值解. 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)；山东省中青年科学家科研奖励基金资助项目(BS2009HZ015)

The alternating group method for KuramotoSivashinsky equation

ZUO Jin-ming¹, ZHANG Yao-ming¹, ZHANG Tian-de², LI Na²

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

Received:2010-12-30 Online:2011-12-20 Published:2011-12-24

摘要/Abstract

摘要：

对KuramotoSivashinsky方程给出了一组非对称的差分格式,用这些差分格式构造了一种适合于并行计算的交替分组方法。证明了方法的线性稳定性。数值试验表明,这种方法在空间方向具有接近四阶的精度。

关键词: Kuramoto-Sivashinsky方程; 并行计算; 交替分组方法; 线性绝对稳定

Abstract:

A group of asymmetric difference schemes to approximate Kuramoto-Sivashinsky equation are given. Using the schemes, the alternating group method for solving Kuramoto-Sivashinsky equation is constructed. The scheme is linear unconditionally stable by analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show the method has near the fourth order ratio of convergence in space.

Key words: Kuramoto-Sivashinsky equation; parallel computation; alternating group method; linear unconditionally stable

左进明1,张耀明1,张天德2,李娜2. KuramotoSivashinsky方程的交替分组方法[J]. J4, 2011, 46(12): 29-32.

ZUO Jin-ming1, ZHANG Yao-ming1, ZHANG Tian-de2, LI Na2. The alternating group method for KuramotoSivashinsky equation[J]. J4, 2011, 46(12): 29-32.

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