Efficient simulation of nonlinear parabolic SPDEs with additive noise
arXiv:1210.8320 · doi:10.1214/10-AAP711
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.
Published in at http://dx.doi.org/10.1214/10-AAP711 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (3)
Cited by in corpus (11)
- A mild Ito formula for SPDEs
- Higher order strong approximations of semilinear stochastic wave equation with additive space-time white noise
- An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
- A full-discrete exponential Euler approximation of invariant measure for parabolic stochastic partial differential equations
- An exponential Wagner-Platen type scheme for SPDEs
- High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise
- Mittag-Leffler Euler integrator for a stochastic fractional order equation with additive noise
- An accelerated exponential time integrator for semi-linear stochastic strongly damped wave equation with additive noise
- Convergence of Density Approximations for Stochastic Heat Equation
- Stochastic evolution equations with Wick-analytic nonlinearities
- Strong error estimates for a fully discrete SAV scheme for the stochastic Allen--Cahn equation with multiplicative noise