Volume 5, Issue 2
Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 229-241.

Published online: 2012-05

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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 $\alpha>0$.

• Keywords

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

26A33, 65M12

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@Article{NMTMA-5-229, author = {}, title = {Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {2}, pages = {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 $\alpha>0$.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m1038}, url = {http://global-sci.org/intro/article_detail/nmtma/5936.html} }
TY - JOUR T1 - Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 229 EP - 241 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m1038 UR - https://global-sci.org/intro/article_detail/nmtma/5936.html KW - Fractional differential equation, Caputo derivative, block-by-block method, convergence analysis. AB -

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 $\alpha>0$.

Jianfei Huang, Yifa Tang & Luis Vázquez. (2020). Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 5 (2). 229-241. doi:10.4208/nmtma.2012.m1038
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