Numerical solution of unsteady state fractional advection–dispersion equation

Abstract

In this article, we find the numerical solution of unsteady state fractional order advection–dispersion equation. For an approximate solution of the proposed problem, we apply Laguerre spectral collocation method and the idea of finite difference method. The proposed method assisted us in reducing the fractional order unsteady state advection–dispersion equation into systems of ordinary differential equations, which we then expressed numerically using finite difference method. Finally, we used examples to test the efficacy of our method, and all of the solutions were compared to the exact solution.

Keywords

• Laguerre spectral collocation method
• Caputo fractional derivative
• finite difference method
• advection–dispersion equations
• error analysis