Recovering the historical distribution for nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity in higher dimensional space

2019 ◽  
Vol 345 ◽  
pp. 114-126 ◽  
Author(s):  
Tran Thi Khieu ◽  
Hoang-Hung Vo
Keyword(s):  
Thermal Conductivity ◽  
Diffusion Equation ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Higher Dimensional ◽  
Historical Distribution ◽  
Space Fractional Diffusion Equation

scholarly journals IMPLEMENTATION OF THE HALF-SWEEP AOR ITERATIVE ALGORITHM FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS

2016 ◽  
Vol 78 (6-4) ◽  
Author(s):  
Andang Sunarto ◽  
Jumat Sulaiman ◽  
Azali Saudi
Keyword(s):  
Diffusion Equation ◽  
Iterative Method ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Implicit Finite Difference Scheme ◽  
Caputo’S Derivative ◽  
Space Fractional Diffusion Equation ◽  
Implicit Finite Difference

In this paper, we consider the numerical solution of one dimensional space-fractional diffusion equation. The half-sweep AOR (HSAOR) iterative method is applied to solve linear system generated from discretization of one dimensional space-fractional diffusion equation using Caputo’s derivative operator and half-sweep implicit finite difference scheme. Furthermore, the formulation and implementation of HSAOR iterative method to solve the problem are also presented. Two examples and comparisons with FSAOR iterative method are given to show the effectiveness of the proposed method. From numerical results obtained, it has shown that the HSAOR iterative method is superior as compared with the FSAOR methods. 

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