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June 2011 Efficient simulation of nonlinear parabolic SPDEs with additive noise
Arnulf Jentzen, Peter Kloeden, Georg Winkel
Ann. Appl. Probab. 21(3): 908-950 (June 2011). DOI: 10.1214/10-AAP711


Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649–667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been introduced. The key idea was to use suitable linear functionals of the noise process in the numerical scheme which allow a higher approximation order to be obtained. Following this approach, a new simplified version of the scheme in the above named reference is proposed and analyzed in this article. The main advantage of the convergence result given here is the higher convergence order for nonlinear parabolic SPDEs with additive noise, although the used numerical scheme is very simple to simulate and implement.


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Arnulf Jentzen. Peter Kloeden. Georg Winkel. "Efficient simulation of nonlinear parabolic SPDEs with additive noise." Ann. Appl. Probab. 21 (3) 908 - 950, June 2011.


Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1223.60050
MathSciNet: MR2830608
Digital Object Identifier: 10.1214/10-AAP711

Primary: 60H15
Secondary: 35R60 , 65C30

Keywords: computational cost , Exponential Euler scheme , linear implicit Euler scheme , Stochastic reaction diffusion equations

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.21 • No. 3 • June 2011
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