The Annals of Applied Probability

Efficient simulation of nonlinear parabolic SPDEs with additive noise

Arnulf Jentzen, Peter Kloeden, and Georg Winkel

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 21, Number 3 (2011), 908-950.

Dates
First available in Project Euclid: 2 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1307020387

Digital Object Identifier
doi:10.1214/10-AAP711

Mathematical Reviews number (MathSciNet)
MR2830608

Zentralblatt MATH identifier
1223.60050

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 65C30: Stochastic differential and integral equations

Keywords
Exponential Euler scheme linear implicit Euler scheme computational cost stochastic reaction diffusion equations

Citation

Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg. Efficient simulation of nonlinear parabolic SPDEs with additive noise. Ann. Appl. Probab. 21 (2011), no. 3, 908--950. doi:10.1214/10-AAP711. https://projecteuclid.org/euclid.aoap/1307020387.


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References

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