Geodesic
Compact ADI method for two-dimensional Riesz space fractional diffusion equation
Filomat, Tome 35 (2021) no. 5, p. 1543

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DOI

In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding fractional derivatives. It is proved that the proposed method is unconditionally stable via the matrix analysis method and the maximum error in achieving convergence is discussed. Numerical example is considered aiming to demonstrate the validity and applicability of the proposed technique.
DOI : 10.2298/FIL2105543V
Classification : 34K28, 65M06, 65M12, 35R11
Keywords: Riesz fractional derivatives, Crank-Nicolson scheme, alternating direction implicit method, unconditionally stable, maximum error 
Sohrab Valizadeh; Alaeddin Malek; Abdollah Borhanifar. Compact ADI method for two-dimensional Riesz space fractional diffusion equation. Filomat, Tome 35 (2021) no. 5, p. 1543 . doi: 10.2298/FIL2105543V
@article{10_2298_FIL2105543V,
     author = {Sohrab Valizadeh and Alaeddin Malek and Abdollah Borhanifar},
     title = {Compact {ADI} method for two-dimensional {Riesz} space fractional diffusion equation},
     journal = {Filomat},
     pages = {1543 },
     year = {2021},
     volume = {35},
     number = {5},
     doi = {10.2298/FIL2105543V},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2105543V/}
}
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