Next Article in Journal
Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
Next Article in Special Issue
Effective Potential from the Generalized Time-Dependent Schrödinger Equation
Previous Article in Journal
Cohen Macaulayness and Arithmetical Rank of Generalized Theta Graphs
Previous Article in Special Issue
Fractional Schrödinger Equation in the Presence of the Linear Potential
Article

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

by 1,†, 2,† and 2,*,†
1
Department of Mathematics, LuLiang University, Lishi 033000, China
2
Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Rui A. C. Ferreira
Mathematics 2016, 4(3), 45; https://doi.org/10.3390/math4030045
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)
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
Show Figures

Figure 1

MDPI and ACS Style

Liu, Y.; Khan, M.; Yan, Y. Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations. Mathematics 2016, 4, 45. https://doi.org/10.3390/math4030045

AMA Style

Liu Y, Khan M, Yan Y. Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations. Mathematics. 2016; 4(3):45. https://doi.org/10.3390/math4030045

Chicago/Turabian Style

Liu, Yanmei, Monzorul Khan, and Yubin Yan. 2016. "Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations" Mathematics 4, no. 3: 45. https://doi.org/10.3390/math4030045

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop