[1]范振成.随机微分方程波形松弛方法的稳定性[J].福建工程学院学报,2014,12(06):586-588.[doi:10.3969/j.issn.1672-4348.2014.06.016]
　Fan Zhencheng.The stability of waveform relaxation methods for stochastic differential equations[J].Journal of FuJian University of Technology,2014,12(06):586-588.[doi:10.3969/j.issn.1672-4348.2014.06.016]
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随机微分方程波形松弛方法的稳定性()
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福建工程学院学报[ISSN:2097-3853/CN:35-1351/Z]

卷:
第12卷
期数:
2014年06期
页码:
586-588
栏目:
出版日期:
2015-01-25

文章信息/Info

Title:
The stability of waveform relaxation methods for stochastic differential equations
作者:
范振成
闽江学院数学系
Author(s):
Fan Zhencheng
Mathematics Department, Minjiang University
关键词:
随机微分方程;  波形松弛方法; 稳定
Keywords:
stochastic differential equation;  waveform relaxation method;  stability
分类号:
O211.63
DOI:
10.3969/j.issn.1672-4348.2014.06.016
文献标志码:
A
摘要:
针对随机微分方程，提出波形松弛方法的稳定性定义，给出了方法稳定的充分条件，证明了方法在给定的条件下是渐进均方稳定的。将得到的定理用于线性随机微分方程，获得了方法的稳定性条件，该条件表明：对应特定分裂函数的波形松弛方法是稳定的。
Abstract:
The stability of waveform relaxation methods of stochastic differential equations was defined with the efficient conditions of the stability. The waveform relaxation methods were proved to be asymptotically mean squared stable under the given conditions. The stable conditions of the linear stochastic differential equations were obtained using the derived theorem. The results show that the waveform relaxation methods are stable for some specifically splitting functions.

参考文献/References:

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[2] Janssen J, Vandewalle S. Multigrid waveform relaxation on spatial finite element meshes: the discretetime case[J]. SIAM J Sci Comput,1996,17 (2): 133–155.
[3] Garrappa R. An analysis of convergence for twostage waveform relaxation methods[J]. J Comput Appl Math, 2004,169: 377-392.
[4] 蒋耀林. 波形松弛方法[M]. 北京: 科学出版社, 2009.
[5] Bao B, Song Y, Shen S. Semiconvergence of parameterized Uzawa waveform relaxation method for a class of differentialalgebraic equations[J]. J Comput Appl Math, 2014, 258: 67-77.
[6] Schurz H, Schneider K R. Waveform relaxation methods for stochastic differential equations[J]. Int J Numer Anal Model,2006,3(2):232-254.
[7] Fan Z. Discrete time waveform relaxation method for stochastic delay differential equations[J]. Appl Math Comput,2010,217(8):3903-3909.
[8] Fan Z. Waveform relaxation method for stochastic differential equations with constant delay[J]. Appl Numer Math,2011,61(2):229-240.

相似文献/References:

[1]范振成.指数波形松弛方法[J].福建工程学院学报,2017,15(04):364.[doi:10.3969/j.issn.1672-4348.2017.04.011]
　Fan Zhencheng.Exponential waveform relaxation methods[J].Journal of FuJian University of Technology,2017,15(06):364.[doi:10.3969/j.issn.1672-4348.2017.04.011]

更新日期/Last Update: 2014-12-25