A linearized second-order finite difference scheme for Riesz space-fractional Allen-Cahn equations with logarithmic free energy

This paper aims to present a linearized second-order finite difference scheme for Allen-Cahn equations with Riesz fractional derivative and logarithmic free energy.First, the discrete maximum bound principle of the proposed scheme is discussed.Second, the discrete energy stability with classical energy is derived.Subsequently, a new discrete energy is defined and proven to be unconditionally decreasing.Finally, a numerical experiment is carried out to verify the theoretical results.