Implicit finite difference solution for time-fractional diffusion equations using AOR method

2014 International Conference on Science & Engineering in Mathematics, Chemistry and Physics

数学;化学;物理学

Sunarto, A.^1 ; Sulaiman, J.^1 ; Saudi, A.^2

School of Science and Technology, Universiti Malaysia, Sabah, Malaysia^1

School of Engineering and Information Technology, Universiti Malaysia, Sabah, Malaysia^2

关键词: Approximation equations;    Coefficient matrix;    Finite difference approximations;    Finite-difference solution;    Fractional derivatives;    Numerical results;    System of linear equations;    Time fractional diffusion equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/495/1/012032/pdf
DOI  :  10.1088/1742-6596/495/1/012032

来源: IOP

【 摘 要 】

In this paper, we derive an implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo's time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large scale and sparse. Due to the characteristics of the coefficient matrix, we use the Accelerated Over-Relaxation (AOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of AOR method. The numerical results of this study show that the proposed iterative method is superior compared with the existing one weighted parameter iterative method.