Abstract
In this article, a hybrid method is developed for solving the time fractional advection–diffusion equation on an unbounded space domain. More precisely, the Chebyshev cardinal functions are used to approximate the solution of the problem over a bounded time domain, and the modified Legendre functions are utilized to approximate the solution on an unbounded space domain with vanishing boundary conditions. The presented method converts solving this equation into solving a system of algebraic equations by employing the fractional derivative matrix of the Chebyshev cardinal functions and the classical derivative matrix of the modified Legendre functions together with the collocation technique. The accuracy of the presented hybrid approach is investigated on some test problems.
Highlights
Mathematical description of physical phenomena in which physical quantities are transferred inside a physical system due to diffusion and convection leads to the well-known advection–diffusion equation [1, 2]
Establishing a hybrid method based on the Chebyshev cardinal functions and the modified Legendre functions for solving this equation
The Chebyshev cardinal functions and the modified Legendre functions are employed to approximate solution of the elicited problem over time and space domains, respectively
Summary
Mathematical description of physical phenomena in which physical quantities are transferred inside a physical system due to diffusion and convection leads to the well-known advection–diffusion equation [1, 2]. The numerical method is presented by using a Lax–Wendroff-type time discretization procedure for solving the fractional advection–diffusion equation [10]. In [22], an efficient shifted Legendre collocation method was proposed for numerical solution of the variableorder fractional Galilei advection–diffusion equation.
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