泛函微分方程波形松弛方法的收敛稳定  

Convergent stability for waveform relaxation methods of functional-di®erential equation

作　　者：范振成 FAN Zhen-cheng(College of Mathematics 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,福建福州350108

出　　处：《高校应用数学学报（A辑）》2020年第1期73-82,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：闽江学院科研项目(MYK19021)。

摘　　要：目前对泛函微分方程波形松弛方法的研究,集中于收敛性.众所周知不稳定的近似方法没有意义,然而罕见关于泛函微分方程松弛方法稳定性的研究工作.首先给出了泛函微分方程波形松弛方法收敛稳定的定义,然后估计波形松弛方法和它的扰动系统生成的两个近似解的差,在常规条件下,推导出差的一个估计.最后利用该估计,得到了泛函微分方程波形松弛方法收敛稳定的充分条件.Now the studies to the waveform relaxation methods of the functional-differential equations(WRMsFDEs)focus on convergence.It is well known that unstable approximating methods are unmeaning.However the few results on the stability of WRMsFDEs are obtained.Firstly,a definition of convergent stability for WRMsFDEs is given.Secondly,by virtue of estimating the difference between the approximating solutions of the waveform relaxation method and its disturbed systems,an estimate is derived under some common conditions.Lastly,the su±cient conditions of the convergent stability of WRMsFDEs are gotten from the above estimate.

关 键 词：泛函微分方程 波形松弛方法 单边LIPSCHITZ条件 收敛稳定 

分 类 号：O241.81[理学—计算数学]