Spectral collocation method for stochastic partial differential equations with fractional Brownian motion

Abstract

In this paper, we consider the numerical approximation of stochastic partial differential equations driven by infinite dimensional fractional Brownian motion with Hurst index H>12. A Fourier spectral collocation approximation is used in space and semi-implicit Euler method is applied for the temporal approximation. Our aim is to investigate the convergence of the proposed method. Optimal strong convergence error estimates in mean-square sense are derived and numerical experiments are presented and confirm theoretical results.