A second-order accurate numerical method for the two-dimensional fractional diffusion equation

2007 ◽  
Vol 220 (2) ◽  
pp. 813-823 ◽  
Author(s):  
Charles Tadjeran ◽  
Mark M. Meerschaert
Keyword(s):  
Diffusion Equation ◽  
Numerical Method ◽  
Fractional Diffusion ◽  
Second Order ◽  
Fractional Diffusion Equation ◽  
Two Dimensional

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.

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