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Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations

Published online by Cambridge University Press:  28 May 2015

Jianfei Huang ,
Yifa Tang  and
Luis Vázquez
Jianfei Huang*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Yifa Tang*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Luis Vázquez*
Affiliation:
Departamento de Matemática Aplicada, Facultad de Informática, Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, 28040-Madrid, Spain
*
Corresponding author.Email address:jfhuang@lsec.cc.ac.cn
Corresponding author.Email address:tyf@lsec.cc.ac.cn
Corresponding author.Email address:lvazquez@fdi.ucm.es
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Abstract

The block-by-block method, proposed by Linz for a kind of Volterra integral equations with nonsingular kernels, and extended by Kumar and Agrawal to a class of initial value problems of fractional differential equations (FDEs) with Caputo derivatives, is an efficient and stable scheme. We analytically prove and numerically verify that this method is convergent with order at least 3 for any fractional order index α > 0.

Keywords

26A3365M12Fractional differential equationCaputo derivativeblock-by-block methodconvergence analysis
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 2 , May 2012 , pp. 229 - 241
Copyright
Copyright © Global Science Press Limited 2012

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