Convex Splitting Runge-Kutta methods for phase-field models

In this paper, we present the Convex Splitting Runge-Kutta (CSRK) methods which provide a simple unified framework to solve phase-field models such as the Allen-Cahn, Cahn-Hilliard, and phase-field crystal equations. The core idea of the CSRK methods is the combination of convex splitting methods and multi-stage implicit-explicit Runge-Kutta methods. Our CSRK methods are high-order accurate in time and we investigate the energy stability numerically. We present numerical experiments to show the accuracy and efficiency of the proposed methods up to the third-order accuracy.