1 Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK 2 TAGC, INSERM-ERM 206, Parc scientifique de Luminy, Case 906, 13288 Marseille cedex 9, France
Abstract:
We consider strong approximations to parabolic stochastic PDEs.We assume the noise lies in a Gevrey space of analytic functions.This type of stochastic forcing includes the case of forcingin a finite number of Fourier modes. We show that with Gevreynoise our numerical scheme has solutions in a discrete equivalentof this space and prove a strong error estimate. Finally wepresent some numerical results for a stochastic PDE with a GinzburgLandaunonlinearity and compare this to the more standard implicitEulerMaruyama scheme.