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

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1543-1554
Author(s):  
Sohrab Valizadeh ◽  
Alaeddin Malek ◽  
Abdollah Borhanifar
Keyword(s):  
Diffusion Equation ◽  
Maximum Error ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Matrix Analysis ◽  
Two Dimensional ◽  
Adi Method ◽  
Space Fractional Diffusion Equation ◽  
The Matrix

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.

scholarly journals Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 39
Author(s):  
Rafał Brociek ◽  
Agata Chmielowska ◽  
Damian Słota
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Parameter Identification ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation ◽  
Swarm Intelligence Algorithm

This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

scholarly journals Mittag-Leffler-Pade approximations for the numerical solution of space and time fractional diffusion equations

2015 ◽  
Vol 4 (4) ◽  
pp. 466 ◽  
Author(s):  
Abdollah Borhanifar ◽  
Sohrab Valizadeh
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Point Of View ◽  
Matrix Analysis ◽  
Space And Time ◽  
The Matrix ◽  
Exponential Relaxation ◽  
Time Fractional Diffusion Equation ◽  
Approximate Scheme

<p>Anomalous diffusion and non-exponential relaxation patterns can be described by a space - time fractional diffusion equation. This paper aims to present a Pade approximation for Mittag-Leffler function mixed finite difference method to develop a numerical method to obtain an approximate solution for the space and time fractional diffusion equation. The truncation error of the method is theoretically analyzed. It is proved that the numerical proposed method is unconditionally stable from the matrix analysis point of view. Finally, some numerical results are given, which demonstrate the efficiency of the approximate scheme.</p>

Sign in / Sign up

Export Citation Format

Share Document