A FAST PARALLEL DIFFERENCE METHOD FOR SOLVING THE TIME-FRACTIONAL GENERALIZED FISHER EQUATION

As a nonlinear fractional reaction-diffusion equation, the Time-Fractional Generalized Fisher (TFGF) equation is deeply rooted in physics, and its fast numerical methods' research has essential scientific significance and practical value. For the time-fractional generalized Fisher equation, based on the alternating segment technique, a parallel computation method for the Fast Alternating Segment Explicit-Implicit (FASE-Ⅰ) difference scheme is proposed. The time-fractional derivative is approximated by the fast L1 algorithm, while the spatial derivative is discretized by the alternating segment explicit-implicit difference method, the nonlinear term is processed using extrapolation. Theoretically analyze the FASE-Ⅰ method's uniqueness, stability, and convergence. Compared with the three classic difference methods, numerical experimental results show that the FASE-Ⅰ method not only has good computational accuracy; but also significantly improves computational efficiency. The FASE-Ⅰ method is efficient and feasible for resolving the time-fractional generalized Fisher equation.