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Fourier spectral methods for some linear stochastic space-fractional partial differential equations

Liu, Yanmei
; 
Khan, Monzorul
; 
Yan, Yubin
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LuLiang University; University of Chester
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2016-07-01
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Mathematics
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Abstract
Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in one-dimensional case are introduced and analyzed. The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of 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 $L^{2}$- norm are obtained. Numerical examples are given.
Citation
Liu, Y., Khan, M., Yan, Y. (2016). Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations. Mathematics, 4(3), 45. DOI: 10.3390/math4030045
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MDPI
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Mathematics
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http://hdl.handle.net/10034/620201
DOI
10.3390/math4030045
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Article
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en
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2227-7390
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http://www.mdpi.com/2227-7390/4/3/45
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