Unconditionally energy decreasing high-order Implicit-Explicit Runge-Kutta methods for phase-field models with the Lipschitz nonlinearity
Phase field models attract much attention these years. The energy naturally decreases along the direction of gradient flows, so it is rather significant for numerical methods to preserve this intrinsic structure. In order to guarantee the energy dissipation, various numerical schemes have been developed and among them, a simple but vital approach is implicit-explicit (IMEX) Runge-Kutta (RK) method. In this paper we prove that a class of high-order IMEX-RK schemes unconditionally preserve the energy dissipation law for phase-field models with Lipschitz nonlinearity. This is the first work to prove that a high-order linear scheme can guarantee the dissipation of the original energy unconditionally. We also obtain the error estimate to show the convergence and accuracy. In the end, we give some IMEX RK schemes as examples.