The aim of this work is to develop a conservative, positivity-preserving (PP), nonlinear finite
volume (FV) scheme for the multi-term nonlocal Nagumo-type equations on distorted …

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 …

In this work, we investigate the two-step backward differentiation formula (BDF2) with
nonuniform grids for the Allen--Cahn equation. We show that the nonuniform BDF2 scheme …

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 …

This paper is concerned with numerical solutions of time-fractional parabolic equations. Due
to the Caputo time derivative being involved, the solutions of equations are usually singular …

In this paper, a second-order scheme with nonuniform time meshes for Caputo–Hadamard
fractional sub-diffusion equations with initial singularity is investigated. Firstly, a Taylor-like …

In this paper, we consider the numerical solutions of the multi-dimensional tempered
fractional integrodifferential equation. First, the second-order backward differentiation …

The discrete gradient structure and the positive definiteness of discrete fractional integrals or
derivatives are fundamental to the numerical stability in long-time simulation of nonlinear …

We establish a unified framework to study the conforming and nonconforming virtual
element methods (VEMs) for a class of time dependent fourth-order reaction–subdiffusion …

Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn
equation has been an open problem in recent years. This work provides a positive answer …