Open AccessCompact ADI method for two-dimensional Riesz space fractional diffusion equation
Author(s) -
Sohrab Valizadeh,
A. Borhanifar,
Alaeddin Malek
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105543v
Subject(s) - mathematics , alternating direction implicit method , discretization , convergence (economics) , mathematical analysis , space (punctuation) , riesz potential , diffusion equation , matrix (chemical analysis) , diffusion , fractional calculus , order (exchange) , finite difference method , linguistics , philosophy , materials science , physics , economy , service (business) , finance , economics , composite material , thermodynamics , economic growth
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.