AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

Numerical methods for the time-fractional diffusion equation: A review

Document Type : Review Article

Authors
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran
Abstract
This review paper focuses on the numerical solution of the time-fractional diffusion equation using various discretization techniques. For the time-fractional derivative, we consider methods such as L-type approximations and Grünwald-Letnikov-based formulas, while for the spatial diffusion term, we utilize the compact finite difference method, finite element method, spectral element method, meshless method, Chebyshev spectral method, and finite block method. In addition, stability and convergence theorems are presented, accompanied by numerical examples that confirm the theoretical results.
Keywords
Subjects

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