A robust numerical method for a fractional differential equation

Zhongdi Cen, Anbo Le and Aimin Xu

Applied Mathematics and Computation, 2017, vol. 315, issue C, 445-452

Abstract: This paper is devoted to giving a rigorous numerical analysis for a fractional differential equation with order α ∈ (0, 1). First the fractional differential equation is transformed into an equivalent Volterra integral equation of the second kind with a weakly singular kernel. Based on the apriori information about the exact solution, an integral discretization scheme on an apriori chosen adapted mesh is proposed. By applying the truncation error estimate techniques and a discrete analogue of Gronwall’s inequality, it is proved that the numerical method is first-order convergent in the discrete maximum norm. Numerical results indicate that this method is more accurate and robust than finite difference methods when α is close to 0.

Keywords: Fractional differential equation; Caputo fractional derivative; Volterra integral equation; Adapted mesh; Convergence analysis (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:315:y:2017:i:c:p:445-452

DOI: 10.1016/j.amc.2017.08.011

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