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IMA Journal of Numerical Analysis 2004 24(4):587-604; doi:10.1093/imanum/24.4.587
© 2004 by Institute of Mathematics and its Applications
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A numerical scheme for stochastic PDEs with Gevrey regularity

Gabriel J. Lord1 and Jacques Rougemont2

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

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 forcing in a finite number of Fourier modes. We show that with Gevrey noise our numerical scheme has solutions in a discrete equivalent of this space and prove a strong error estimate. Finally we present some numerical results for a stochastic PDE with a Ginzburg–Landau nonlinearity and compare this to the more standard implicit Euler–Maruyama scheme.

Key Words: stochastic partial differential equations; Gevrey regularity; strong error estimate

Received 6 August 2002. Revised 28 October 2003.


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