Spectral approximation of a new class of stochastic fractional evolution equations

TL;DR

This paper introduces a spectral and quadrature-based numerical method for approximating a new class of fractional parabolic stochastic evolution equations, with proven error bounds and verified through numerical experiments.

Contribution

It presents a novel spectral approximation approach for fractional stochastic PDEs, including error analysis and practical validation.

Findings

Strong error bounds established for spectral and temporal discretizations.

Numerical experiments confirm the effectiveness of the proposed method.

Abstract

A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in spatial statistics. A truncation of the spectral basis function expansion is used to discretise in space, and then a quadrature is used to approximate the temporal evolution of each basis coefficient. Strong error bounds are proved both for the spectral and temporal approximations. The method is tested and the results are verified by several numerical experiments.