scholarly journals Finite difference approximation of space-fractional diffusion problems: The matrix transformation method

2017 ◽  
Vol 73 (2) ◽  
pp. 261-269 ◽  
Author(s):  
Béla J. Szekeres ◽  
Ferenc Izsák
Keyword(s):  
Finite Difference ◽  
Transformation Method ◽  
Fractional Diffusion ◽  
Finite Difference Approximation ◽  
Matrix Transformation ◽  
Difference Approximation ◽  
The Matrix ◽  
Diffusion Problems

Compact Crank–Nicolson and Du Fort–Frankel Method for the Solution of the Time Fractional Diffusion Equation

2015 ◽  
Vol 12 (06) ◽  
pp. 1550041 ◽  
Author(s):  
Faoziya Al-Shibani ◽  
Ahmad Ismail
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Finite Difference Methods ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
The One

In this paper, two compact implicit finite difference methods are developed and analyzed for solving the one-dimensional time fractional diffusion equation. The temporal derivative is approximated by using Grünwald–Letnikov formula. Compact finite difference approximation is used for the second-order derivative in space. The local truncation errors are discussed. The stability analysis and the convergence of the proposed methods are investigated by means of Fourier series method. A comparison between the results of these methods and the exact solution is made. Numerical tests are given to verify the feasibility and accuracy of the methods.

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