In this paper, we mainly study a reduced‐order finite difference (FD) method with an extra
modified term for the Allen–Cahn equation with a small parameter perturbation and a …

In this paper, we consider the numerical simulation of the binary fluid–surfactant phase field
model coupled with geometric curvature on the curved surface. By taking account of the …

The reaction-diffusion model can generate a wide variety of spatial patterns, which has been
widely applied in chemistry, biology, and physics, even used to explain self-regulated …

In this paper, the discontinuous finite volume element method (DFVEM) is considered to
solve the Allen-Cahn equation which contains strong nonlinearity. The method is based on …

In this paper, we present two types of unconditionally maximum principle preserving finite
element schemes to the standard and conservative surface Allen–Cahn equations. The …

In this paper, we propose an explicit hybrid numerical method for solving the Allen–Cahn
equation, which models antiphase domain coarsening process in a binary mixture. The …

It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, ie, the
free-energy functional decreases in time. Linearly implicit integrators have been developed …

Abstract The Allen–Cahn equation is one of fundamental equations of phase-field models,
while the logarithmic Flory–Huggins potential is one of the most useful energy potentials in …

Over the years, energy-dissipation-preserving (EDP) numerical methods (EDP-NMs) for the
nonlinear system of energy dissipation have attracted considerable attention because they …

In this paper, a new linearized high-order compact difference method is presented for
numerical simulation of three dimensional (3D) Allen–Cahn equation with three kinds of …