scholarly journals A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain

2018 ◽  
Vol 77 ◽  
pp. 114-121 ◽  
Author(s):  
Wenping Fan ◽  
Fawang Liu
Keyword(s):  
Diffusion Equation ◽  
Numerical Method ◽  
Convex Domain ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Space Fractional Diffusion Equation ◽  
Distributed Order

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 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.

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