Parallel finite-difference algorithms for three-dimensional space-fractional diffusion equation with $$\psi $$-Caputo derivatives

2020 ◽  
Vol 39 (3) ◽  
Author(s):  
V. O. Bohaienko
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Caputo Derivatives ◽  
Space Fractional Diffusion Equation ◽  
Three Dimensional Space

A New Numerical Scheme for the Space Fractional Diffusion Equation

2014 ◽  
Vol 599-601 ◽  
pp. 1305-1308 ◽  
Author(s):  
Jun Ying Cao ◽  
Zi Qiang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Efficient Method ◽  
Numerical Scheme ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation

We construct the numerical method of the space fractional diffusion equation in this paper. We propose an efficient method for its numerical solution. This method is based on a finite difference in time and finite element method in space. Convergence of the method is rigorously established. A series of numerical examples are provided to support the theoretical claims.

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