Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations

Yanmei Liu, Monzorul Khan and Yubin Yan
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Yanmei Liu: Department of Mathematics, LuLiang University, Lishi 033000, China
Monzorul Khan: Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
Yubin Yan: Department of Mathematics, University of Chester, Chester CH1 4BJ, UK

Mathematics, 2016, vol. 4, issue 3, 1-28

Abstract: Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of the Laplacian subject to some boundary conditions. We approximate the space-time white noise by using piecewise constant functions and obtain the approximated stochastic space-fractional partial differential equations. The approximated stochastic space-fractional partial differential equations are then solved by using Fourier spectral methods. Error estimates in the L 2 -norm are obtained, and numerical examples are given.

Keywords: space-fractional partial differential equations; stochastic partial differential equations; Fourier spectral method; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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