A transformed L1 method for solving the multi-term time-fractional diffusion problem

Mianfu She, Dongfang Li and Hai-wei Sun

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 193, issue C, 584-606

Abstract: In this paper, we present a novel scheme for solving a time-fractional initial–boundary value problem, where the equation contains a sum of Caputo derivatives with orders between 0 and 1. In order to overcome the difficulty of initial layer, we introduce a change of variable in the temporal direction and investigate the regularity of the solutions of the resulting system. A modified L1 approximation is used to approximate the Caputo derivatives and a standard Galerkin-Spectral method is applied to approximate the spatial derivatives. Unconditional stability and convergence of the fully-discrete scheme are proved by applying a novel discrete fractional Grönwall inequality. Finally, numerical examples are given to confirm our theoretical results.

Keywords: Multi-term time-fractional equation; Modified L1 scheme; Chebyshev–Galerkin spectral method; Error estimates (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:193:y:2022:i:c:p:584-606

DOI: 10.1016/j.matcom.2021.11.005

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