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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 = {Pin Lyu, Seakweng Vong and Zhibo Wang}, 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 AU - Pin Lyu, Seakweng Vong & Zhibo Wang 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 and Zhibo Wang. (2018). 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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