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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 139530, 6 pages
http://dx.doi.org/10.1155/2013/139530
Research Article

A Spectral Deferred Correction Method for Fractional Differential Equations

1College of Mathematics, Qingdao University, Qingdao 266071, China
2National Laboratory for Scientific Computing, MCTI, Avenida Getulio Vargas 333, 25651-075 Petropolis, RJ, Brazil

Received 31 May 2013; Revised 7 August 2013; Accepted 19 September 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 Jia Xin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.