The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

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 …

The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

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 …

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 …

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

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 …

In this paper, we propose and analyze a second order efficient numerical scheme for the
time fractional L^ 2 L 2 gradient flows. The proposed scheme is based on scalar auxiliary …

In this work, an efficient alternating direction implicit (ADI) finite difference scheme is
proposed to solve the three-dimensional time-fractional telegraph equation. The fully …