An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients

2021 ◽  
Vol 402 ◽  
pp. 126091
Author(s):  
Kejia Pan ◽  
Hai-Wei Sun ◽  
Yuan Xu ◽  
Yufeng Xu
Keyword(s):  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Multigrid Solver ◽  
Fractional Diffusion Equations

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Eid Doha ◽  
Ali Bhrawy ◽  
Samer Ezz-Eldien
Keyword(s):  
Numerical Technique ◽  
Operational Matrix ◽  
Fractional Diffusion ◽  
High Accuracy ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Algebraic Equations ◽  
Fractional Differentiation ◽  
Fractional Diffusion Equations ◽  
General Method

AbstractIn this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

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