Efficient simulation of nonlinear parabolic SPDEs with additive noise

TL;DR

This paper introduces a simplified numerical scheme for simulating nonlinear parabolic SPDEs with additive noise, achieving higher convergence order while maintaining simplicity in implementation.

Contribution

It proposes a new, simplified scheme based on linear functionals of noise, improving convergence order for nonlinear SPDEs with additive noise.

Findings

Higher convergence order demonstrated for the scheme

Scheme is simple to implement and simulate

Applicable to nonlinear parabolic SPDEs with additive noise

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.