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Mathematics 2016, 4(3), 45; doi:10.3390/math4030045

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

1,†
,
2,†
and
2,†,*
1
Department of Mathematics, LuLiang University, Lishi 033000, China
2
Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Rui A. C. Ferreira
Received: 13 March 2016 / Revised: 13 June 2016 / Accepted: 15 June 2016 / Published: 1 July 2016
(This article belongs to the Special Issue Fractional Differential and Difference Equations)
View Full-Text   |   Download PDF [920 KB, uploaded 1 July 2016]   |  

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. View Full-Text
Keywords: space-fractional partial differential equations; stochastic partial differential equations; Fourier spectral method; error estimates space-fractional partial differential equations; stochastic partial differential equations; Fourier spectral method; error estimates
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Liu, Y.; Khan, M.; Yan, Y. Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations. Mathematics 2016, 4, 45.

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