Numerical Algorithm for Space-Fractional Diffusion Equations via PAOR
Andang Sunarto and Jumat Sulaiman
1.IAIN Bengkulu, Indonesia.
2.Faculty of Science and Natural Resources,
Universiti Malaysia Sabah, Malaysia.
Abstract
In this study, we examines the effectiveness of the Preconditioned Accelerated Over-Relaxation (PAOR) iterative method together with an unconditionally implicit finite difference approximation equation to solve space-fractional diffusion equations (SFDE-s) by using the Caputo-s space-fractional derivative. For this, the implicit approximation equation and preconditioned matrix are used to construct the corresponding preconditioned linear system in which its coefficient matrix is large scale and sparse. Then, formulation and implementation the PAOR iterative method are also presented. Based on numerical algorithm results of the proposed iterative method, it can be concluded that the proposed iterative method (PAOR) is superior to the PSOR and PGS iterative methods.
Keywords: PAOR, Space-fractional diffusion equations, Implicit finite difference, Caputo-s
Topic: Mathematics