2,523
Views
84
CrossRef citations to date
0
Altmetric
Reviews

Numerical methods for fractional partial differential equations

&
Pages 1048-1099 | Received 21 Feb 2017, Accepted 22 May 2017, Published online: 04 Jul 2017
 

ABSTRACT

In this review paper, we are mainly concerned with the finite difference methods, the Galerkin finite element methods, and the spectral methods for fractional partial differential equations (FPDEs), which are divided into the time-fractional, space-fractional, and space-time-fractional partial differential equations (PDEs). Besides, fast algorithms for the FPDEs are included in order to stimulate more efficient algorithms for high-dimensional FPDEs.

2010 AMS SUBJECT CLASSIFICATIONS:

Acknowledgments

The authors wish to thank Professor Abdul Q. M. Khaliq, Editor-in-Chief of International Journal Computer Mathematics for his cordial invitation. The authors are also grateful to Professor Khaliq and the referees for the valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was partially supported by the National Natural Science Foundation of China under grant nos. [11372170, 11671251, and 11632008].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.