TY - JOUR
T1 - Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations
AU - Jianfei Huang, Yifa Tang & Luis Vázquez
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 - <p style="text-align: justify;">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 $\alpha&gt;0$.</p>