The Sinc–Legendre collocation method for a class of fractional convection–diffusion equations with variable coefficients

This paper deals with the numerical solution of classes of fractional convection–diffusion equations with variable coefficients. The fractional derivatives are described based on the Caputo sense. Our approach is based on the collocation techniques. The method consists of reducing the problem to the solution of linear algebraic equations by expanding the required approximate solution as the elements of shifted Legendre polynomials in time and the Sinc functions in space with unknown coefficients. The properties of Sinc functions and shifted Legendre polynomials are then utilized to evaluate the unknown coefficients. Several examples are given and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

► The fractional convection–diffusion equation with variable coefficients is investigated.
► A collocation approach based on Sinc functions and Legendre polynomials is presented to find its solution.
► The method consists of reducing the problem to the solution of linear algebraic equations.
► The method is tested on several examples to demonstrate its validity and applicability.