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Volume 7, Issue 4
A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation

Pin Lyu, Seakweng Vong & Zhibo Wang

DOI: 10.4208/eajam.181016.300517e

East Asian J. Appl. Math., 7 (2017), pp. 752-766.

Published online: 2018-02

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  • 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.

  • Keywords

Boundary value problem, Caputo fractional derivative, Finite difference method, Convergence, Derivative bound.

  • AMS Subject Headings

65L10, 65L12, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-752, author = {}, title = {A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181016.300517e}, url = {http://global-sci.org/intro/article_detail/eajam/10718.html} }
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 -

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.

Pin Lyu, Seakweng Vong & Zhibo Wang. (2020). A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation. East Asian Journal on Applied Mathematics. 7 (4). 752-766. doi:10.4208/eajam.181016.300517e
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