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

In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme,
which aims at solving nonlinear problems quickly, is considered to numerically solve the …

We put forward and analyze the high-order (up to fourth) strong stability-preserving implicit-
explicit Runge-Kutta schemes for the time integration of the space-fractional Allen-Cahn …

In this work, we present a second-order nonuniform time-stepping scheme for the time-
fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete …

In this paper, we consider the numerical study for the multi-dimensional fractional-in-space
Allen-Cahn equation with homogeneous Dirichlet boundary condition. By utilizing Strang's …

In this work, we propose a Crank--Nicolson-type scheme with variable steps for the time
fractional Allen--Cahn equation. The proposed scheme is shown to be unconditionally …

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing
a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable …

Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-
implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's …

In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …

We construct and analyze the variable-step scheme to efficiently solve the space-time
fractional Cahn–Hilliard equation in two dimensions. The associated variational energy …