Energy-decreasing second order exponential time differencing Runge-Kutta methods for Nonlocal Cahn-Hilliard equation

Due to the energetic variational structure inherent in the nonlocal phase field model, the energy of the system naturally decreases over time according to the Nonlocal Cahn-Hilliard (NCH) equation. Preserving this crucial property of energy dissipation is highly desirable in numerical solutions. However, most existing numerical methods can only ensure a decrease in some modified form of energy, rather than the original energy itself. In this paper, we propose the second-order exponential time differencing Runge-Kutta (ETD-RK2) methods for solving the NCH equation. We demonstrate that this method has the ability to unconditionally preserve the original energy dissipation. Numerical experiments are included to illustrate the accuracy and energy stability of the ETD-RK2 methods.