The purpose of this paper is to investigate a space-time Sinc-collocation method for solving
the fourth-order nonlocal heat model arising in viscoelasticity, which is a class of partial …

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 …

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

A generalised fractional derivative (the ψ-Caputo derivative) is studied. Generalisations of
standard discretisations are constructed for this derivative: L1, L1-2, L2-1 σ for derivatives of …

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 …

This paper is concerned with the unconditionally optimal H 1-error estimate of a fast second-
order scheme for solving nonlinear subdiffusion equations on the nonuniform mesh. We use …

A new discrete energy dissipation law of the variable-step fractional BDF2 (second-order
backward differentiation formula) scheme is established for time-fractional Cahn-Hilliard …