Finite difference and spectral collocation methods for the solution of semilinear time fractional convection-reaction-diffusion equations with time delay (Q2008082)

The authors consider nonlinear fractional convection-reaction-diffusion equations with time delay. They show how to construct an efficient numerical method for it. The time fractional deriative is discretized by a second-order finite difference and the spatial derivative is discretized by a Chebyshev spectral collocation method. Next, it is shown that the fully discrete scheme is unconditionally stable and convergent. Further, they provide extensive numerical results complementing the theory. Hence, it is illustrated that the present method is accurate and efficient.