Numerical Solution of Stochastic Nonlinear Differential Equations using Wiener-Hermite Expansion

机译：Wiener-Hermite扩展的随机非线性微分方程的数值解

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In this work, the Wiener-Hermite Expansion (WHE) is used in solving nonlinear differential equations with stochastic excitations. The generation of the equivalent set of deterministic integro-differential equations is described. A numerical Picard's successive algorithm is suggested to solve the resulting system. The suggested algorithm is applied on the 1D diffusion equation and the results are compared with the WHEP (WHE with perturbation) technique. The current work shows that the WHE solutions are the limit of the WHEP solutions with infinite number of corrections. The suggested algorithms are shown to be efficient in estimating the stochastic response of the nonlinear systems.

机译：在这项工作中，Wiener-Hermite膨胀（Whe）用于用随机激励求解非线性微分方程。描述了等同的确定性积分微分方程的产生。建议使用数值图霸的连续算法来解决所得系统。建议的算法应用于1D扩散方程，并将结果与WHEP（WHE具有扰动）技术进行比较。目前的工作表明，WHE解决方案是具有无限校正的WHEP解决方案的极限。建议的算法显示在估计非线性系统的随机响应时是有效的。

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《International Conference of Numerical Analysis and Applied Mathematics》|2014年||共4页
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A. S. Al-Johani; M. A. El-Beltagy;
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中图分类计量学;
关键词
Nonlinear D.E.; Stochastic D.E.; Wiener-Hermite expansion; Picard's algorithm;

机译：非线性D.E。;随机D.E。;Wiener-Hermite扩展;Picard的算法;

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1. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion [J] . Mohamed A.El-Beltagy, Noha A.Al-Mulla Journal of applied mathematics . 2014,第2期

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2. Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion [J] . Mohamed A.El-Beltagy, Noha A.Al-Mulla Journal of applied mathematics . 2014,第1期

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3. On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations [J] . E Weinan, Hutzenthaler Martin, Jentzen Arnulf, Journal of Scientific Computing . 2019,第3期

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4. Numerical Solution of Stochastic Nonlinear Differential Equations using Wiener-Hermite Expansion [C] . A. S. Al-Johani, M. A. El-Beltagy International Conference of Numerical Analysis and Applied Mathematics . 2014

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5. Wiener Chaos Expansion and Numerical Solutions of Stochastic Partial Differential Equations [D] . Luo, Wuan. 2006

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Numerical Solution of Stochastic Nonlinear Differential Equations using Wiener-Hermite Expansion

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