An efficient numerical scheme and its stability analysis for a time-fractional reaction diffusion model

Abstract

An efficient numerical scheme is presented to solve a time-fractional reaction–diffusion (TFRD) model with Caputo temporal–fractional derivative. The L1 scheme is employed to approximate the Caputo temporal–fractional derivative and a collocation method based on sextic B-spline (SBS) basis functions is used for discretization of the spatial variable. The stability of the method is investigated. Three numerical examples are provided to illustrate the performance and accuracy of the method. The convergence order of proposed method is O(Δt2−α+Δx6), where α is the order of fractional derivative (FD) (0<α<1) and Δt and Δx represent, respectively, the temporal step size and the spatial mesh size. The influence of the order of fractional derivative α on the solution profile is examined. The computed results and CPU times are compared with those obtained by the standard second-order finite difference method.