In this paper, modified variational iteration algorithm-II is investigated for finding approximate
solutions of nonlinear Parabolic equations. Comparisons of the MVIA-II with trigonometric B …

We consider numerical methods for solving the fractional-in-space Allen–Cahn equation
which contains small perturbation parameters and strong nonlinearity. A standard fully …

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 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 …

This paper is concerned with the generalized Allen–Cahn equation with a nonlinear mobility
that may be degenerate, which also includes an advection term appearing in many …

In this article, modified versions of variational iteration algorithms are presented for the
numerical simulation of the diffusion of oil pollutions. Three numerical examples are given to …

A high-order and energy stable scheme is developed to simulate phase-field models by
combining the semi-implicit spectral deferred correction (SDC) method and the energy …

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the
Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization …

Pattern is a non-uniform macro structure with some regularity in space or time, which is
common in nature. In this manuscript, we introduce the Fourier transform for spatial …

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 …