Year: 2021
Author: Yongtao Zhou, Chengjian Zhang, Huiru Wang
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 108–129
Abstract
This paper deals with the numerical computation and analysis for Caputo fractional differential equations (CFDEs). By combining the $p$-order boundary value methods (BVMs) and the $m$-th Lagrange interpolation, a type of extended BVMs for the CFDEs with $\gamma$-order ($0 <\gamma < 1$) Caputo derivatives are derived. The local stability, unique solvability and convergence of the methods are studied. It is proved under the suitable conditions that the convergence order of the numerical solutions can arrive at $\min\left\{p, m-\gamma+1\right\}$. In the end, by performing several numerical examples, the computational efficiency, accuracy and comparability of the methods are further illustrated.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1907-m2018-0252
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 108–129
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fractional differential equations Caputo derivatives Boundary value methods Local stability Unique solvability Convergence.