A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation. Issue 4 (31st January 2018)

• Record Type: Journal Article
• Authors: Lyu, Pin; Vong, Seakweng; Wang, Zhibo
• Is Part Of: East Asian journal on applied mathematics. Volume 7:Issue 4(2017)
• Page Start: 752
• Page End: 766
• Publication Date: 2018-01-31
• Subjects: 65L10, -- 65L12, -- 65L20; Boundary value problem, -- Caputo fractional derivative, -- Finite difference method, -- Convergence, -- Derivative bound; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.181016.300517e
• Languages: English
• ISSNs: 2079-7362

Abstract

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.