Numerical approximation of nonlinear SPDE’s

The numerical analysis of stochastic parabolic partial differential equations of the form d u + A ( u ) d t = f d t + g d W , is surveyed, where A is a nonlinear partial operator and W a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framew...

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Bibliographic Details
Published in:Stochastic partial differential equations : analysis and computations 2023-12, Vol.11 (4), p.1553-1634
Main Authors: Ondreját, Martin, Prohl, Andreas, Walkington, Noel J.
Format: Article
Language:English
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Parabolic differential equations
Partial Differential Equations
Probability Theory and Stochastic Processes
Statistical Theory and Methods
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Summary:The numerical analysis of stochastic parabolic partial differential equations of the form d u + A ( u ) d t = f d t + g d W , is surveyed, where A is a nonlinear partial operator and W a 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.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-022-00271-9