In this paper, we consider numerical approximation of the Allen–Cahn equation with double
well potential, which is a fundamental equation in phase-field models. We propose a novel …

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 …

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for
numerical schemes? To the best of our knowledge, the state-of-art stability framework is the …

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time
stepping schemes, which are based on the newly developed Invariant Energy …

In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …

This letter introduces novel linear relaxation schemes for solving the phase field models,
particularly the Allen–Cahn (AC) type and Cahn–Hilliard (CH) type equations. The proposed …

Compared with the well-known classical Allen–Cahn equation, the modified Allen–Cahn
equation, which is equipped with a nonlocal Lagrange multiplier or a local-nonlocal …

In this paper, we propose a new linear second-order finite difference scheme for Allen–Cahn
equations. We use a modified Leap-Frog finite difference scheme with stabilized term and a …

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time
stepping schemes, which are based on the newly developed invariant energy quadratization …

It is well known that the classic Allen–Cahn equation satisfies the maximum bound principle
(MBP), that is, the absolute value of its solution is uniformly bounded for all time by certain …