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 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 survey is given of convergence results that have been proved when the L1 scheme is
used to approximate the Caputo time derivative Dα t (where 0< α< 1) in initial-boundary …

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 …

We propose a positivity-preserving finite volume scheme on non-conforming quadrilateral
distorted meshes with hanging nodes for subdiffusion equations, where the differential …

We consider a time-fractional Cahn–Hilliard equation where the conventional first-order time
derivative is replaced by a Caputo fractional derivative of order. Based on an a priori bound …

The positive definiteness of real quadratic forms with convolution structures plays an
important role in stability analysis for time-stepping schemes for nonlocal operators. In this …

A fast, accurate, and stable numerical algorithm is proposed to solve the anisotropic phase-
field dendritic crystal growth model. The algorithm combines the first-order direction splitting …

The positive definiteness of discrete time-fractional derivatives is fundamental to the
numerical stability (in the energy sense) for time-fractional phase-field models. A novel …

In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional
Allen-Cahn equation in the Caputo's form. The L1 implicit scheme is shown to preserve a …