A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise

Details A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise

2011-06-09

arxiv.org/abs/1106.1889v2

Mathematics

Numerical Analysis

This article has been accepted for publication in Numerical Algorithms

Scientific paper

In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a higher order than the well-known linear implicit Euler scheme. In comparison to the infinite dimensional analog of Milstein type scheme recently proposed in [Jentzen & R\"{o}ckner (2012); A Milstein scheme for SPDEs, Arxiv preprint arXiv:1001.2751v4], our scheme is easier to implement and needs less computational effort due to avoiding the derivative of the diffusion function. The new scheme can be regarded as an infinite dimensional analog of Runge-Kutta method for finite dimensional stochastic ordinary differential equations (SODEs). Numerical examples are reported to support the theoretical results.

Affiliated with

Also associated with

No associations

Rating

A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Runge-Kutta type scheme for nonlinear stochastic partial differential equations with multiplicative trace class noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-580937