Computational modelling
Zahra Mahboob Dana; Hashem Saberi Najafi; Amir Hossein Refahi Sheikhani
Abstract
In this paper, a one-dimensional fractional advection-diffusion equation is considered. First, we propose a numerical approximation of the Riemann-Liouville fractional derivative which is fourth-order accurate, then a numerical method for the fractional advection-diffusion equation using a high order ...
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In this paper, a one-dimensional fractional advection-diffusion equation is considered. First, we propose a numerical approximation of the Riemann-Liouville fractional derivative which is fourth-order accurate, then a numerical method for the fractional advection-diffusion equation using a high order finite difference scheme is presented. It is proved that the scheme is convergent. The stability analysis of numerical solutions is also discussed. The method is applied in several examples and the accuracy of the method is tested in terms of error norm. Furthermore, the numerical results have been compared with some other methods.
