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

Part of:Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  31 January 2018

Pin Lyu,
Seakweng Vong and
Zhibo Wang
Pin Lyu*
Affiliation:
Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
Seakweng Vong*
Affiliation:
Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
Zhibo Wang*
Affiliation:
School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, Guangdong, China
*
*Corresponding author. Email addresses:lyupin1991@163.com (P. Lyu), swvong@umac.mo (S. Vong), wzbmath@gdut.edu.cn (Z. Wang)
*Corresponding author. Email addresses:lyupin1991@163.com (P. Lyu), swvong@umac.mo (S. Vong), wzbmath@gdut.edu.cn (Z. Wang)
*Corresponding author. Email addresses:lyupin1991@163.com (P. Lyu), swvong@umac.mo (S. Vong), wzbmath@gdut.edu.cn (Z. Wang)

Abstract

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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 problemCaputo fractional derivativeFinite difference methodConvergenceDerivative bound

MSC classification

Secondary:65L10: Boundary value problems65L12: Finite difference methods65L20: Stability and convergence of numerical methods

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017, pp. 752 - 766
Copyright
Copyright © Global-Science Press 2017 

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