A linearly decoupled second-order finite difference scheme for ternary Allen-Cahn equations (pp.510-533)

In this paper, we construct a new linearly second-order finite difference scheme to solve the ternary Allen-Cahn equation.We use the modified Crank-Nicolson/Adams-Bashforth scheme with a stabilized term for time and a central finite difference scheme for space.We prove that the numerical solutions satisfy the discrete maximum bound principle (MBP) and energy stability under reasonable constraints on the time step size and coefficient of stabilized term.Based on the MBP, the maximum-norm error estimates are rigorously analyzed.Several numerical experiments are performed to verify the theoretical results.