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 …

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional
subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where …

For the time-fractional phase-field models, the corresponding energy dissipation law has not
been well studied on both the continuous and the discrete levels. In this work, we address …

In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-
order multi-term subdiffusion equation. The L1 method on graded meshes is employed in …

This paper proposes a linearized fast high-order time-stepping scheme to solve the time–
space fractional Schrödinger equations. The time approximation is done by using the fast L2 …

Alikhanov's high-order scheme for Caputo fractional derivatives of order α ∈ (0, 1) α∈(0, 1)
is generalised to nonuniform meshes and analysed for initial-value problems (IVPs) and …

For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …

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 …

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 …