Difference methods for stochastic partial differential equations

Roth C.

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Difference methods for stochastic partial differential equations

机译：随机偏微分方程的差分方法

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The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Ito-type, in particular hyperbolic equations. The main notions of deterministic difference methods, i.e. convergence, consistency, and stability, are developped for the stochastic case. It is shown that the proposed stochastic difference schemes for several partial differential equations have these properties. [References: 8]

机译：本文着重于使用差分方法来近似求解Ito型随机偏微分方程，特别是双曲型方程的解。确定性差异方法的主要概念，即收敛性，一致性和稳定性，是针对随机情况而提出的。结果表明，所提出的几个偏微分方程的随机差分格式都具有这些性质。 [参考：8]

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2002年第12期|共10页
作者
Roth C.;
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正文语种 eng
中图分类应用数学;
关键词
Stochastic partial differential equations of ito-type; Difference methods; Convergence; Consistency; Stability;

机译：ito型随机偏微分方程;差分方法;收敛性;一致性;稳定性;

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专利

1. A Combination of Finite Difference and Wong-Zakai Methods for Hyperbolic Stochastic Partial Differential Equations [J] . Christian Roth Stochastic Analysis and Applications . 2006,第1期

机译：双曲型随机偏微分方程的有限差分和Wong-Zakai方法的组合
2. Numerical solution of time-dependent stochastic partial differential equations using RBF partition of unity collocation method based on finite difference [J] . Esmaeilbeigi M., Chatrabgoun O., Shafa M. Engineering analysis with boundary elements . 2019,第JULa期

机译：基于有限差分的统一配置方法RBF划分的时变随机偏微分方程数值解
3. Numerical solution of time-dependent stochastic partial differential equations using RBF partition of unity collocation method based on finite difference [J] . Esmaeilbeigi M., Chatrabgoun O., Shafa M. Engineering analysis with boundary elements . 2019,第Jula期

机译：基于有限差异的Unity Collocation方法RBF分区的时间依赖随机偏微分方程的数值解
4. The stability of neutral stochastic partial differential difference equations [C] . Yu-Tian Zhang, Qi Luo . 2004

机译：中立型随机偏微分差分方程的稳定性
5. Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations. [D] . Jin, Chao. 2007

机译：随机偏微分方程的并行域分解方法和非线性积分方程的分析。
6. Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage [O] . Paul Johnson, Sydney Howell, Peter Duck -1

机译：随机动态优化的偏微分方程方法：在储能风力发电中的应用
7. Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines [O] . McDonald Stuart 2006

机译：线性随机偏微分方程的线性有限差分逼近

Difference methods for stochastic partial differential equations

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