In this paper, we design, analyze and numerically validate an unconditionally energy stable
second order numerical method for solving the Allen–Cahn equation which represents a …

In this article, we present a second-order in time implicit–explicit (IMEX) local discontinuous
Galerkin (LDG) method for computing the Cahn–Hilliard equation, which describes the …

Two semi-implicit numerical methods are proposed for solving the surface Allen-Cahn
equation which is a general mathematical model to describe phase separation on general …

We study uniform bounds associated with the Allen–Cahn equation and its numerical
discretization schemes. These uniform bounds are different from, and weaker than, the …

In this paper, we consider the adaptive finite element method for the Allen–Cahn equation.
The adaptive method is based on a second order accurate unconditionally energy stable …

We present numerical simulations for the surface Cahn–Hilliard equation which describes
phase separation phenomenon occurred on general surfaces. The spatial discretization is …

In this paper, we present a fourth-order difference scheme for solving the Allen-Cahn
equation in both 1D and 2D. The proposed scheme is described by the compact difference …

In this paper, we consider the numerical study for the multi-dimensional fractional-in-space
Allen-Cahn equation with homogeneous Dirichlet boundary condition. By utilizing Strang's …

In this paper, we exploit the Strang splitting technique for solving the multidimensional Allen-
Cahn equations with anisotropic spatial fractional Riesz derivatives. Fully discrete numerical …

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 …