… It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, ie, …
stabilization are studied in [7], [8]. Other methods used in the literature include the implicit-explicit …

… We propose an explicit stable finite difference method (FDM) for the Allen–Cahn (AC)
equation. The AC … is used to solve some implicit parts of the nonlinear equation in their papers. …

… where L denotes the linear operator (for example, L = −Δ2 for Cahn-Hilliard and L = Δ for
Allen-Cahn) and N(u) collects the nonlinear part. In its most generality one should think of N(u) …

… -order (up to fourth) strong stability-preserving implicit-explicit Runge-Kutta schemes for the
… Allen-Cahn equation, which inherits the maximum principle preserving and energy stability. …

… approximation of the Allen–Cahn equation with double well potential, which is a fundamental
equation in phase-field models. We propose a novel linear, energy stable and maximum …

… the equation is how to treat the nonlinear and … implicit–explicit Runge–Kutta method. We
show analytically that the scheme is uniquely solvable and unconditionally energy stable by …

… stabilization terms, mollifying the nonlinearity or … methods date back to the work of Chen
and Shen [4] in which a semi-implicit Fourier spectral method was implemented on a Allen-Cahn …

… equation, which is a nonlinear partial differential equation. For this reason, many numerical
… stability of the AC equation under the infinity norm can be established for the implicit–explicit …

… By modifying the nonlinear parts in the governing equation, we have a … equation. In
addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit …

… The main contribution of this paper is to prove the stability and error … for the Allen–Cahn
equation (1.1)–(1.2). Since the implicit treatment of the nonlinear item u 3 results in a nonlinear …