波形松弛方法的稳定性  

STABILITY OF WAVEFORM RELAXATION METHODS

作　　者：范振成 Fan Zhencheng(College of mathematic and data science,Minjiang University,Fuzhou 350108,China)

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》2023年第2期180-197,共18页Journal on Numerical Methods and Computer Applications

基　　金：福建省自然科学基金(2021J011031);福建省发树慈善基金会研究专项(MFK23013)资助。

摘　　要：波形松弛(WR)方法是求解微分方程的一种重要数值方法,迄今为止,关于它的研究集中于收敛性,罕有对其稳定性的研究.提出了常微分方程WR方法稳定的定义.借鉴常微分方程经典数值方法稳定性的常规研究方法,研究WR方法的稳定性,给出了连续WR方法保持三种标准试验方程稳定性的充分条件.使用Lyapunov技巧研究WR方法的压缩性,得到了连续和离散WR方法保持试验方程压缩的充分条件.The waveform relaxation(WR)method is an important numerical method to solve differential equations.So far,the investigations of the behaviour of WR methods focus on the convergence and few studies of stability are published.In this paper we present the definition of WR methods for ordinary differential equations(ODEs).By applying the standard techniques used to study stable properties of classical numerical methods of ODEs,we investigate the stability properties of WR methods and give the sufficient conditions under which the continuous WR methods can preserve the stable properties of three standard test equations.The contraction properties of WR methods are investigated by Lyapunov techniques and some sufficient conditions of preserving the contraction properties of the test equations are obtained for continuous and discrete time WR methods.

关 键 词：常微分方程 波形松弛方法 稳定 压缩 LYAPUNOV方法 

分 类 号：O241.8[理学—计算数学]