Second-order error analysis of a corrected average finite difference scheme for time-fractional Cable equations with nonsmooth solutions

Yongtao Zhou and Wei Xu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 631-644

Abstract: In this paper, we first formulate an average finite difference scheme with appropriate correction terms for the time-fractional initial-value problem of y′(t)+0RLDt1−αy(t)=g(t), where 0RLDt1−α denotes the Riemann–Liouville fractional derivative of order 1−α(α∈(0,1)). It is shown that, under some suitable conditions on the data, the numerical solution converges to the exact solution with order O(τ2), where τ is the time step size. The method is then extended to solve the time-fractional Cable equation, combined with a standard discretisation of the spatial derivatives on a uniform mesh. The second-order time convergence rate is proved. Several numerical examples are given to illustrate the good agreement with the theoretical analysis of the presented methods.

Keywords: Second-order error analysis; Corrected average finite difference scheme; Time-fractional Cable equation; Nonsmooth solution; Correction terms (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:631-644

DOI: 10.1016/j.matcom.2024.07.029

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