A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation

A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

  1. Superconvergence Analysis of Anisotropic FEMs for Time Fractional Variable Coefficient Diffusion Equations

    Wei, Yabing | Zhao, Yanmin | Wang, Fenling | Tang, Yifa | Yang, Jiye

    Bulletin of the Malaysian Mathematical Sciences Society, Vol. 43 (2020), Iss. 6 P.4411

    https://doi.org/10.1007/s40840-020-00929-4 [Citations: 4]
  2. A numerical framework for the approximate solution of fractional tumor-obesity model

    Arshad, Sadia | Baleanu, Dumitru | Defterli, Ozlem |

    International Journal of Modeling, Simulation, and Scientific Computing, Vol. 10 (2019), Iss. 01 P.1941008

    https://doi.org/10.1142/S1793962319410083 [Citations: 5]