文章基本信息

标题：Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations
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作者：Leonid E Shaikhet ; Jason A Roberts
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2006
卷号：2006
期号：1
页码：073897
DOI：10.1155/ADE/2006/73897
语种：English
出版社：Hindawi Publishing Corporation
摘要：We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation , where α, β, σ, τ ≥ 0 are real constants, and W(t) is a standard Wiener process. The areas of the regions of asymptotic stability for the class of methods considered, indicated by the sufficient conditions for the discrete system, are shown to be equal in size to each other and we show that an upper bound can be put on the time-step parameter for the numerical method for which the system is asymptotically mean-square stable. We illustrate our results by means of numerical experiments and various stability diagrams. We examine the extent to which the continuous system can tolerate stochastic perturbations before losing its stability properties and we illustrate how one may accurately choose a numerical method to preserve the stability properties of the original problem in the numerical solution. Our numerical experiments also indicate that the quality of the sufficient conditions is very high.
关键词：Numerical Experiment ; Functional Equation ; Original Problem ; Asymptotic Stability ; Stability Property