What question did this study set out to answer?

The aim is to introduce and analyze a numerical method for approximating fractional parabolic stochastic evolution equations.

February 21, 2026Open Access

Spectral approximation of a class of stochastic time-fractional evolution equations

Key Points

The aim is to introduce and analyze a numerical method for approximating fractional parabolic stochastic evolution equations.
Develop a spectral basis function expansion to discretize spatially.
Utilize quadrature to approximate temporal evolution of basis coefficients.
Prove strong error bounds for both spectral and temporal approximations.
Conduct numerical experiments to validate the proposed method.
Strong error bounds are established for the spectral and temporal approximations.
The method's efficacy is confirmed through various numerical experiments.

Abstract

A method for numerical approximation of a 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.

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