Abstract and Applied Analysis

A Spectral Deferred Correction Method for Fractional Differential Equations

Jia Xin, Jianfei Huang, Weijia Zhao, and Jiang Zhu

Full-text: Open access

Abstract

A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 139530, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450393

Digital Object Identifier
doi:10.1155/2013/139530

Mathematical Reviews number (MathSciNet)
MR3121412

Zentralblatt MATH identifier
1297.65080

Citation

Xin, Jia; Huang, Jianfei; Zhao, Weijia; Zhu, Jiang. A Spectral Deferred Correction Method for Fractional Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 139530, 6 pages. doi:10.1155/2013/139530. https://projecteuclid.org/euclid.aaa/1393450393


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