Compact ADI method for solving two-dimensional Riesz space fractional diffusion equation
Numerical Analysis
2020-04-21 v4 Numerical Analysis
Abstract
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. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed technique.
Cite
@article{arxiv.1802.02015,
title = {Compact ADI method for solving two-dimensional Riesz space fractional diffusion equation},
author = {Sohrab Valizadeh and Alaeddin Malek and Abdollah Borhanifar},
journal= {arXiv preprint arXiv:1802.02015},
year = {2020}
}
Comments
16 pages, 2 tables, This article has not been published in any journals