色散方程的交替分组迭代方法

色散方程的交替分组迭代方法

刘洪华

山东大学数学与系统科学学院，山东济南250100

收稿日期:2006-04-27 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 刘洪华

The alternating group iterative method for the dispersive equation

LIU Hong-hua

School of Math. and System Sci., Shandong Univ., Jinan 250100, Shandong, China

Received:2006-04-27 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: LIU Hong-hua

摘要/Abstract

摘要： 给出了求解具有周期边界条件色散方程近似解的交替分组迭代法.构造了逼近色散方程的两层隐式差分格式,以此隐式差分格式为基础设计出一种适合在并行机上进行计算的交替分组迭代方法,并证明了上述隐式差分格式的绝对稳定性和交替分组迭代过程的收敛性.数值试验对色散方程的隐格式与Crank-Nicolson格式分别应用交替分组迭代求解.结果表明,该方法具有很好的数值精度和良好的实用性.

关键词: 色散方程, 交替分组迭代方法, 并行计算 , 绝对稳定

Abstract: The alternating group iterative method for the dispersive equation with periodic boundary condition is presented. A twolevel implicit difference scheme is designed, and an alternating group iterative method is suggested which is capable of parallelism on parallel computer. In addition, unconditional stability of the difference scheme and convergence of the iterative process are proved. The alternating group iterative method is used to solve the implicit scheme and the Crank-Nicolson scheme of the dispersive equation. The results show that this method has good accuracy and practicability.

Key words: parallel computation , unconditionally stable, alternating group iterative method, dispersive equation

中图分类号:

O241.82

刘洪华 . 色散方程的交替分组迭代方法[J]. J4, 2007, 42(1): 19-23 .

LIU Hong-hua . The alternating group iterative method for the dispersive equation[J]. J4, 2007, 42(1): 19-23 .

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