A High Accuracy Numerical Method Based on Interpolation Technique for Time-Fractional Advection-Diffusion Equations

In this paper, the time-fractional advection-diffusion equation (TFADE) is solved by the barycentric Lagrange interpolation collocation method (BLICM). In order to approximate the fractional derivative under the definition of Caputo, BLICM is used to approximate the unknown function. We obtain the discrete scheme of the equation by combining BLICM with the Gauss-Legendre quadrature rule. The convergence rate for the TFADE equation of the BLICM is derived, and the accuracy of the discrete scheme can be improved by modifying the number of Gaussian nodes. To illustrate the efficiency and accuracy of the present method, a few numerical examples are presented and compared with the other existing methods.