Abstract
In this study, we propose approximate algorithm solution of the space-fractional diffusion equation (SFDE's) based on a quarter-sweep (QS) implicit finite difference approximation equation. To derive this approximation equation, the Caputo's space-fractional derivative has been used to discretize the proposed problems. By using the Caputo's finite difference approximation equation, a linear system will be generated and solved iteratively. In addition to that, formulation and implementation algorithm the Quarter-Sweep AOR (QSAOR) iterative method are also presented. Based on numerical results of the proposed iterative method, it can be concluded that the proposed iterative method is superior to the FSAOR and HSAOR iterative method.
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