We consider a one‐dimensional Allen‐Cahn equation with constraint from the viewpoint of
numerical analysis. The constraint is provided by the subdifferential of the indicator function …

In 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an
alternative to the Allen-Cahn model for the description of phase field transformations. With …

In a numerical study, we consider the Allen–Cahn equation with a double-obstacle
constraint. The constraint is a multivalued function that is provided by the subdifferential of …

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In this chapter, as mentioned in Chapter 1, to understand the idea of the discrete variational
derivative method (DVDM)[29], we design a structure-preserving finite difference scheme for …

We consider numerical methods for solving the fractional-in-space Allen-Cahn (FiSAC)
equation which contains small perturbation parameters and strong noninearilty. Standard …

In this paper, an efficient stabilized algorithm based on the linear Crank-Nicolson/Adams-
Bashforth scheme is proposed to solve the viscous Cahn-Hilliard equation. In this algorithm …

In this paper, a linear second order numerical scheme is developed and investigated for the
Allen-Cahn equation with a general positive mobility. In particular, our fully discrete scheme …

We study the systematic numerical approximation of a class of Allen-Cahn type problems
modeling the motion of phase interfaces. The common feature of these models is an …

In this paper, we use finite difference methods for solving the Allen–Cahn equation which
contains small perturbation parameters and strong nonlinearity. We consider a linearized …