Mixed Generalized Jacobi and Chebyshev Collocation Method for Time-Fractional Convection-Diffusion Equations

Abstract:

      In this paper, we study an efficient higher order numerical method to time-fractional partial differential equations with temporal Caputo derivative. A collocation method based on shifted generalized Jacobi functions is taken for approximating the solution of the given time-fractional partial differential equation in time and a shifted Chebyshev collocation method based on operational matrix in space. The derived numerical solution can approximate the non-smooth solution in time of given equations well. Some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.