Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran
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 Grunwald-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.
Ghoreyshi, A. , Abbaszadeh, M. and Dehghan, M. (2026). Numerical methods for the time-fractional diffusion equation: A review. AUT Journal of Mathematics and Computing, 7(2), 213-269. doi: 10.22060/ajmc.2026.24592.1441
MLA
Ghoreyshi, A. , , Abbaszadeh, M. , and Dehghan, M. . "Numerical methods for the time-fractional diffusion equation: A review", AUT Journal of Mathematics and Computing, 7, 2, 2026, 213-269. doi: 10.22060/ajmc.2026.24592.1441
HARVARD
Ghoreyshi, A., Abbaszadeh, M., Dehghan, M. (2026). 'Numerical methods for the time-fractional diffusion equation: A review', AUT Journal of Mathematics and Computing, 7(2), pp. 213-269. doi: 10.22060/ajmc.2026.24592.1441
CHICAGO
A. Ghoreyshi , M. Abbaszadeh and M. Dehghan, "Numerical methods for the time-fractional diffusion equation: A review," AUT Journal of Mathematics and Computing, 7 2 (2026): 213-269, doi: 10.22060/ajmc.2026.24592.1441
VANCOUVER
Ghoreyshi, A., Abbaszadeh, M., Dehghan, M. Numerical methods for the time-fractional diffusion equation: A review. AUT Journal of Mathematics and Computing, 2026; 7(2): 213-269. doi: 10.22060/ajmc.2026.24592.1441
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