Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises

Hdl Handle:
http://hdl.handle.net/10034/620636
Title:
Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises
Authors:
Liu, Fang; Yan, Yubin; Khan, Monzorul
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.
Affiliation:
Lvliang University, University of Chester
Citation:
Liu, F., Yan, Y. & Khan, M. (2018-forthcoming). Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises. Journal of Computational Analysis and Applications.
Publisher:
Springer
Journal:
Journal of Computational Analysis and Applications
Publication Date:
Feb-2018
URI:
http://hdl.handle.net/10034/620636
Additional Links:
https://link.springer.com/journal/10819
Type:
Article
Language:
en
Description:
The final publication is available at link.springer.com via http://dx.doi.org/[insert DOI]
ISSN:
1521-1398
EISSN:
1572-9206
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Fangen
dc.contributor.authorYan, Yubinen
dc.contributor.authorKhan, Monzorulen
dc.date.accessioned2017-09-28T10:56:04Z-
dc.date.available2017-09-28T10:56:04Z-
dc.date.issued2018-02-
dc.identifier.citationLiu, F., Yan, Y. & Khan, M. (2018-forthcoming). Fourier spectral methods for stochastic space fractional partial differential equations driven by special additive noises. Journal of Computational Analysis and Applications.en
dc.identifier.issn1521-1398-
dc.identifier.urihttp://hdl.handle.net/10034/620636-
dc.descriptionThe final publication is available at link.springer.com via http://dx.doi.org/[insert DOI]en
dc.description.abstractFourier 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.en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urlhttps://link.springer.com/journal/10819en
dc.subjectSpace fractional partial differential equationsen
dc.subjectstochastic partial differential equationsen
dc.subjectFourier spectral methoden
dc.subjecterror estimatesen
dc.titleFourier spectral methods for stochastic space fractional partial differential equations driven by special additive noisesen
dc.typeArticleen
dc.identifier.eissn1572-9206-
dc.contributor.departmentLvliang University, University of Chesteren
dc.identifier.journalJournal of Computational Analysis and Applicationsen
dc.date.accepted2017-09-10-
or.grant.openaccessYesen
rioxxterms.funderunfundeden
rioxxterms.identifier.projectunfunded researchen
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2019-02-28-
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