Barycentric interpolation collocation method based on Crank-Nicolson scheme for the Allen-Cahn equation

This paper proposes a numerical scheme for the Allen-Cahn equation that represents a phenomenological model for anti-phase domain coarsening in a binary mixture. In order to obtain a high order discretization in space, we adopt the barycentric interpolation collocation method. The semi-discretized scheme in space is shown to be consistent. The second-order Crank-Nicolson scheme is used for temporal discretization and the simple iteration method is adopted for nonlinear term. Corresponding algebraic system is derived. Numerical examples are demonstrated to validate the efficiency of the proposed method.