The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds

Authors:
P. E. Kloeden;G. J. Lord;A. Neuenkirch;T. Shardlow
Affiliations:
Institut für Mathematik, Goethe-Universität Frankfurt, D-60325 Frankfurt a.M., Germany;Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK;Fakultät für Mathematik, TU Dortmund, D-44227 Dortmund, Germany;School of Mathematics, University of Manchester, Manchester M13 9PL, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 1
Cited 3

Postprocessing for Stochastic Parabolic Partial Differential Equations

SIAM Journal on Numerical Analysis

Almost sure convergence of a Galerkin approximation for SPDEs of Zakai type driven by square integrable martingales

Journal of Computational and Applied Mathematics
On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

Journal of Computational Physics
A Runge---Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise

Numerical Algorithms

Quantified Score

Hi-index	7.30

Visualization

Abstract

We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher).