arXiv subjects

Sohrab Valizadeh

Publications and source records attributed to Sohrab Valizadeh.

2 recordsLinked to original sources

arXiv2021

General matrix transform method for the Riesz space fractional advection-dispersion equations

In this paper, a mixed high order finite difference scheme-Padé approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference scheme that derived from fractional centered difference and Padé approximation method for space and time integration, respectively. The stability analysis of the proposed method is discussed via theoretical matrix analysis. Numerical experiments are carried out to confirm the theoretical results of the proposed method.

math.NA↗

arXiv2020

Compact ADI method for solving two-dimensional Riesz space fractional diffusion equation

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.

math.NA↗