The reaction–diffusion equations models on surfaces have received growing interest and
have been applied to simulate the physical processes and chemical reactions on ultra-thin …

In this work, the fundamental design procedure, termed as Algorithms by Design, is
exploited to establish novel explicit algorithms under the umbrella of linear multi-step (LMS) …

Purpose The purpose of this paper is to propose an efficient space-time operator-splitting
method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the …

In this paper, we investigate numerical solution of Allen–Cahn equation with constant and
degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize …

In this paper, superconvergent analysis of an efficient two-grid method is discussed for the
Allen–Cahn equation with the nonconforming EQ 1 rot finite element. The unconditional …

In this paper, we consider a class of multiscale methods for the solution of nonlinear problem
in perforated domains. These problems are of multiscale nature and their discretizations …

In this paper, we mainly study a new Crank-Nicolson finite difference (FD) method with a
large time step for solving the nonlinear phase-field model with a small parameter …

We propose a structure-preserving finite difference scheme for the Allen–Cahn equation
with a dynamic boundary condition using the discrete variational derivative method [9]. In …

In this paper, a high order accurate spectral method is presented for the space-fractional
diffusion equations. Based on Fourier spectral method in space and Chebyshev collocation …

In this paper, a viscous Cahn-Hilliard equation with logarithmic Flory-Huggins energy
potential is solved numerically by using a convex splitting scheme. This numerical scheme is …