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非线性随机Pantograph微分方程及其θ-方法的均方渐近稳定性 被引量：1

Mean-Square Asymptotic Stability of θ-Methods for Nonlinear Stochastic Pantograph Differential Equations
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摘要 本文主要研究了非线性随机Pantograph微分方程,讨论了其零解的均方渐近稳定性并给出了零解均方渐近稳定的充分条件.在本文的第三部分,我们将随机θ-方法应用于这类问题,获得了数值解均方渐近稳定条件. This paper studies mean-square asymptotic stability of the zero solution of initial problems of a general class of stochastic pantograph differential equation. The sufficient conditions of mean-square asymptotic stability of the zero solution are derived. In the third section, numerical methods based on θ- methods are suggested and mean-square asymptotic stability conditions for the presented methods are derived.
作者 肖飞雁 张诚坚
机构地区 华中科技大学数学与统计学院
出处 《应用数学》 CSCD 北大核心 2009年第1期199-203,共5页 Mathematica Applicata
基金 国家自然科学基金资助项目(10871078)
关键词 非线性随机 Pantograph微分方程 均方渐近稳定 Θ-方法 Nonlinear stochastic Pantograph differential equation Mean-square asymptotic stability θ- method
分类号 O175.13 [理学—基础数学] O241.8 [理学—计算数学]
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参考文献7

  • 1Cao W,Liu M,Fan Z. MS-stability of the Euler-Maruyama method for stochastic differential dalay equations[J]. Appl. Math. Comp. , 2004,159:127-135.
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二级参考文献15

  • 1Baker C T H,Buckwar E.Continuous θ-methods for the stochastic pantograph equation[J].Electron.Trans.Numer.Anal.,2000,11:131--151.
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  • 8Cao W R,Liu M Z,Fan Z C.MS-stability of the Euler-Maruyama method for stochastic differential delay equations[J].Appl.Math.Comp.,2004,159:127-135.
  • 9Kloeden P E,Platen E.Numerical Solution of Stochastic Differential Equations[M].Belin:Springer-Verlag,1992.
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应用数学
2009年 第1期

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