Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 : pp. 752–766
Abstract
In this paper, we consider a two-point boundary value problem with Caputo fractional derivative, where the second order derivative of the exact solution is unbounded. Based on the equivalent form of the main equation, a finite difference scheme is derived. The $L_∞$ convergence of the difference system is discussed rigorously. The convergence rate in general improves previous results. Numerical examples are provided to demonstrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.181016.300517e
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 4 : pp. 752–766
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Boundary value problem Caputo fractional derivative Finite difference method Convergence Derivative bound.