gL 1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations

Xuhao Li and Patricia J. Y. Wong
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Xuhao Li: School of Mathematical Sciences, Anhui University, Hefei 230601, China
Patricia J. Y. Wong: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore

Mathematics, 2022, vol. 10, issue 8, 1-14

Abstract: In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α . The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL 1 scheme . The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is ( 2 − α ) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.

Keywords: generalized fractional derivative; time-diffusion problem; generalized linear interpolation; numerical scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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