gL1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations

Mathematics

Patricia J. Y. Wong¹  Xuhao Li² 

[1] School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;School of Mathematical Sciences, Anhui University, Hefei 230601, China;

关键词: generalized fractional derivative;    time-diffusion problem;    generalized linear interpolation;    numerical scheme;   

DOI  :  10.3390/math10081219

来源: DOAJ

【 摘 要 】

In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order $\alpha$. The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL1 scheme. The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is $(2-\alpha )$ for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.

【 授权许可】

Unknown