A linearly stabilized convolution quadrature method for the time-fractional Allen–Cahn equation

Abstract

This paper proposes a linearly stabilized convolution quadrature method for solving the time-fractional Allen–Cahn equation. The stability condition is explicitly given such that the method is unconditionally stable for any time step size. The space is discretized by the central difference method. We prove that the fully discrete scheme preserves the discrete maximum principle, the discrete energy is bounded, and the modified discrete energy decays monotonically. Numerical simulations support the theoretical analysis.