Loading...
Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises
Liu, Fang Yan, Yubin Khan, Monzorul
Liu, Fang
Yan, Yubin
Khan, Monzorul
Advisors
Editors
Other Contributors
Affiliation
EPub Date
Publication Date
2018-02-28
Submitted Date
Collections
Files
Loading...
Main article
Adobe PDF, 221.7 KB
Other Titles
Abstract
Fourier spectral methods for solving stochastic space fractional partial differential
equations driven by special additive 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. The space-time noise is approximated by the piecewise constant
functions in the time direction and by some appropriate approximations in the space direction. The
approximated stochastic space fractional partial differential equations are then solved by using Fourier
spectral methods. For the linear problem, we obtain the precise error estimates in the $L_{2}$ norm and find the relations between the error bounds and the fractional powers. For the nonlinear problem, we introduce the numerical algorithms and MATLAB codes based on the FFT transforms. Our numerical algorithms can be adapted easily to solve other stochastic space fractional partial differential equations with multiplicative noises. Numerical examples for the semilinear stochastic space fractional partial differential equations are given.
Citation
Liu, F., Yan, Y. & Khan, M. (2018). Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises. Journal of Computational Analysis and Applications, 24(2), 290-309
Publisher
EudoxusPress
Journal
Journal of Computational Analysis and Applications
Research Unit
DOI
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
Series/Report no.
ISSN
1521-1398
EISSN
1572-9206