A fast time stepping Legendre spectral method for solving fractional Cable equation with smooth and non-smooth solutions

Yibin Xu, Yanqin Liu, Xiuling Yin, Libo Feng, Zihua Wang and Qiuping Li

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 211, issue C, 154-170

Abstract: To improve the calculation accuracy and efficiency, in this article, we develop a fast time stepping Legendre spectral method for solving fractional Cable equation, where in temporal direction the time stepping method is utilized and the spatial variable is discretized by Legendre spectral method. The time stepping method is used to approximate fractional order derivative, and its convergence accuracy in time is O(τ2). The fast algorithm is applied to the time stepping method and it can reduce the computational complexity from O(M2) to O(MlogM), where M denotes the number of time stepping. For non-smooth solutions, we deal with the initial singularity by adding correction terms. We also analyze the numerical stability and convergence in detail. Numerical experiments confirm our theoretical analysis and efficiency of the fast algorithm.

Keywords: Time stepping method; Legendre spectral method; Stability and convergence; Fast algorithm; Smooth and non-smooth solutions (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:211:y:2023:i:c:p:154-170

DOI: 10.1016/j.matcom.2023.04.009

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