Numerical approximation of nonlinear SPDE’s
Numerical approximation of nonlinear SPDE’s
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DOI：
10.1007/s40072-022-00271-9
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发表时间：
2020-03
期刊：
影响因子：
--
通讯作者：
Martin Ondreját;A. Prohl;N. Walkington
中科院分区：
文献类型：
--
作者：
Martin Ondreját;A. Prohl;N. Walkington
The numerical analysis of stochastic parabolic partial differential equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$\end{document}is surveyed, whereAis a nonlinear partial operator andWa Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.
The numerical analysis of stochastic parabolic partial differential equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$\end{document}is surveyed, whereAis a nonlinear partial operator andWa Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.