Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:273

Article

Gracia, J. L.^1,2  Stynes, M.³ 

[1] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

[2] Univ Zaragoza, Dept Appl Math, E-50009 Zaragoza, Spain

[3] Natl Univ Ireland Univ Coll Cork, Dept Math, Cork, Ireland

关键词: Fractional differential equation;    Caputo fractional derivative;    Convective term;    Boundary value problem;    Finite difference method;    Convergence proof;   

DOI  :  10.1016/j.cam.2014.05.025

来源: Elsevier

【 摘 要 】

A rigorous numerical analysis is given for a fractional derivative two-point boundary value problem. The highest-order term of the differential operator is a Caputo fractional derivative of order delta is an element of (1, 2). The second and higher-order derivatives of the solution of the problem are in general unbounded at one end of the interval, which creates difficulties for the analysis. The problem is discretized on an equidistant mesh of diameter h using delta standard central difference approximation of the convection term, and nodal convergence of order 0(h(delta-1)) is proved provided that h satisfies a stability condition that depends on S and the convective coefficient. This condition may be restrictive when delta is near 1; when it is violated the solution may exhibit small oscillations, but these can be removed by a simple and inexpensive postprocessing technique. Numerical results are given to display the performance of the method. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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