TY - JOUR
T1 - A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 752
EP - 766
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.181016.300517e
UR - https://global-sci.org/intro/article_detail/eajam/10718.html
KW - Boundary value problem, Caputo fractional derivative, Finite difference method, Convergence, Derivative bound.
AB - <p style="text-align: justify;">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.</p>