Numerical Solution of Stochastic Partial Differential Equations with Correlated Noise
Numerical Analysis
2013-11-12 v1
Abstract
In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By applying a spectral Galerkin method for spatial discretization and a numerical scheme in time introduced by Jentzen Kloeden, we obtain the rate of path-wise convergence in the uniform topology. The main assumptions are either uniform bounds on the spectral Galerkin approximation or uniform bounds on the numerical data. Numerical examples illustrate the theoretically predicted convergence rate.
Keywords
Cite
@article{arxiv.1311.2207,
title = {Numerical Solution of Stochastic Partial Differential Equations with Correlated Noise},
author = {Dirk Blömker and Minoo Kamrani},
journal= {arXiv preprint arXiv:1311.2207},
year = {2013}
}