Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation

2019 ◽  
Vol 166 ◽  
pp. 494-507
Author(s):  
Yang Xu ◽  
Yanming Zhang ◽  
Jingjun Zhao
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Galerkin Methods ◽  
Space Fractional Diffusion Equation ◽  
Spectral Galerkin Methods

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.

A New Numerical Method for the Riesz Space Fractional Diffusion Equation

2011 ◽  
Vol 213 ◽  
pp. 393-396 ◽  
Author(s):  
Heng Fei Ding ◽  
Yu Xin Zhang ◽  
Wan Sheng He ◽  
Xiao Ya Yang
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Analytic Solution ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Transform Method ◽  
Unconditionally Stable ◽  
Space Fractional Diffusion Equation ◽  
The Difference

Firstly, using matrix transform method, we transform the Riesz space fractional diffusion equation into an ordinary differential equation, and get its analytic solution. Secondly, we use (2,1) Pade approxiation to the exponentinal matrix of the analytic solution and obtain a new difference scheme for solving Riesz space fractional diffusion equation. Finally, we prove that the difference scheme is unconditionally stable.

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