Arbitrarily high-order energy stable s-stage RK-IEQ scheme for the nonlocal Cahn–Hilliard equation

Abstract

In this paper, for solving the nonlocal-type Cahn–Hilliard equation, we propose an arbitrary high-order energy stable s-stage RK-IEQ scheme, which is based on the combination of the Invariant Energy Quantization (IEQ) approach and the s-stage Runge–Kutta method. We prove that the proposed scheme is unconditionally energy stable and carry out several numerical examples in both 2D and 3D to demonstrate the accuracy and stability of the scheme.