A Spectral Deferred Correction Method for Fractional Differential Equations

A Spectral Deferred Correction Method for Fractional Differential Equations

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...

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Main Authors: Jia Xin, Jianfei Huang, Weijia Zhao, Jiang Zhu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/139530
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spelling doaj-2c977ec3afc34ff5877bdab266b5af972020-11-24T23:28:50ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/139530139530A Spectral Deferred Correction Method for Fractional Differential EquationsJia Xin0Jianfei Huang1Weijia Zhao2Jiang Zhu3College of Mathematics, Qingdao University, Qingdao 266071, ChinaCollege of Mathematics, Qingdao University, Qingdao 266071, ChinaCollege of Mathematics, Qingdao University, Qingdao 266071, ChinaNational Laboratory for Scientific Computing, MCTI, Avenida Getulio Vargas 333, 25651-075 Petropolis, RJ, BrazilA 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.http://dx.doi.org/10.1155/2013/139530
collection DOAJ
language English
format Article
sources DOAJ
author Jia Xin
Jianfei Huang
Weijia Zhao
Jiang Zhu
spellingShingle Jia Xin
Jianfei Huang
Weijia Zhao
Jiang Zhu
A Spectral Deferred Correction Method for Fractional Differential Equations
Abstract and Applied Analysis
author_facet Jia Xin
Jianfei Huang
Weijia Zhao
Jiang Zhu
author_sort Jia Xin
title A Spectral Deferred Correction Method for Fractional Differential Equations
title_short A Spectral Deferred Correction Method for Fractional Differential Equations
title_full A Spectral Deferred Correction Method for Fractional Differential Equations
title_fullStr A Spectral Deferred Correction Method for Fractional Differential Equations
title_full_unstemmed A Spectral Deferred Correction Method for Fractional Differential Equations
title_sort spectral deferred correction method for fractional differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/139530
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AT jianfeihuang aspectraldeferredcorrectionmethodforfractionaldifferentialequations
AT weijiazhao aspectraldeferredcorrectionmethodforfractionaldifferentialequations
AT jiangzhu aspectraldeferredcorrectionmethodforfractionaldifferentialequations
AT jiaxin spectraldeferredcorrectionmethodforfractionaldifferentialequations
AT jianfeihuang spectraldeferredcorrectionmethodforfractionaldifferentialequations
AT weijiazhao spectraldeferredcorrectionmethodforfractionaldifferentialequations
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