An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis

The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) based on a spectral Tau method. An extension of the operational approach of the Tau method with the orthogonal polynomial bases is proposed to convert FDEs to its matrix–vect...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011, Vol.61 (1), p.30-43
Main Authors: Ghoreishi, F., Yazdani, S.
Format: Article
Language:English
Subjects:
Caputo derivative
Computer simulation
Convergence
Derivatives
Differential equations
Fractional differential equations
Mathematical models
Multiplication
Norms
Operational approach to the Tau method
Representations
Spectra
Tau method
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) based on a spectral Tau method. An extension of the operational approach of the Tau method with the orthogonal polynomial bases is proposed to convert FDEs to its matrix–vector multiplication representation. The fractional derivatives are described in the Caputo sense. The spectral rate of convergence for the proposed method is established in the L 2 norm. We tested our procedure on several examples and observed that the obtained numerical results confirm the theoretical prediction of the exponential rate of convergence.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.10.027