Numerical analysis of semilinear stochastic evolution equations in Banach spaces

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Abstract

The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.

Details

Original languageEnglish
Pages (from-to)485-516
Number of pages32
JournalJournal of Computational and Applied Mathematics
Volume147.2002
Issue number2
DOIs
Publication statusPublished - 2002