Finite difference and spectral collocation methods for the solution of semilinear time fractional convection-reaction-diffusion equations with time delay

In this paper, an efficient numerical method is constructed to solve the nonlinear fractional convection-reaction-diffusion equations with time delay. Firstly, we discretize the time fractional derivative with a second order finite difference scheme. Then, Chebyshev spectral collocation method is utilized to space component and to obtain full discretization of problem. We show that the proposed method is unconditionally stable and convergent. Numerical experiments are carried out to demonstrate the accuracy of the proposed method and to compare the results with analytical solutions and the numerical solutions of other schemes in the literature. The results show that the present method is accurate and efficient. It is illustrated that the numerical results are in good agreement with theoretical ones.