Numerical approximation for the fractional advection-diffusion equation using a high order difference scheme
نویسندگان
1 Department of applied mathematics, Faculty of mathematical sciences, Lahijan branch, Islamic Azad University, Lahijan, Iran
2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
3 Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
doi
10.22105/jarie.2021.240340.1183چکیده
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.
