A Split-Step Predictor–Corrector Method for Space-Fractional Reaction–Diffusion Equations with Nonhomogeneous Boundary Conditions

Abstract

A split-step second-order predictor–corrector method for space-fractional reaction–diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence. The matrix transfer technique is used for spatial discretization of the problem. The method is shown to be unconditionally stable and second-order convergent. Numerical experiments are performed to confirm the stability and second-order convergence of the method. The split-step predictor–corrector method is also compared with an IMEX predictor–corrector method which is found to incur oscillatory behavior for some time steps. Our method is seen to produce reliable and oscillation-free results for any time step when implemented on numerical examples with nonsmooth initial data. We also present a priori reliability constraint for the IMEX predictor–corrector method to avoid unwanted oscillations and show its validity numerically.