基于线性多步法的波形松弛方法的线性稳定性  

Stability of Waveform Relaxation Methods Based on Linear Multistep Methods

作　　者：范振成 Fan Zhencheng

机构地区：[1]闽江学院数学与数据科学学院,福州350108

出　　处：《数值计算与计算机应用》2020年第1期58-67,共10页Journal on Numerical Methods and Computer Applications

基　　金：闽江学院科研项目(MYK19021).

摘　　要：波形松弛(WR)方法的研究成果丰富,但主要集中于收敛性,罕见关于稳定性的研究.研究基于线性多步法的WR方法的线性稳定性,获得了线性稳定的几个充分条件,给出了一些具体的线性稳定WR方法的例子,并提供了一些支持理论结果的数值算例.There exist a variety of research works on waveform relaxation(WR)methods.Most of them focus on the convergence and few of them is concerned about the stability.In this paper the linear stability of WR methods based on the linear multistep methods is studied.We have obtained some sufficient conditions of the linear stability,given some examples of the linearly stable WR methods,and presented some numerical examples for supporting the theories obtained.

关 键 词：稳定 线性稳定 波形松弛方法 线性多步法 

分 类 号：O241.8[理学—计算数学]