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

Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations
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Year:    2012

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 229–241

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 $\alpha>0$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2012.m1038

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 229–241

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Fractional differential equation Caputo derivative block-by-block method convergence analysis.

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