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 …

An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal
model. The suggested method is proved to preserve a modified energy dissipation law at the …

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 …

In this work, we are concerned with the stability and convergence analysis of the second-
order backward difference formula (BDF2) with variable steps for the molecular beam …

The two-step backward differential formula (BDF2) with unequal time-steps is applied to
construct an energy stable convex-splitting scheme for the Cahn–Hilliard model. We focus …

In this paper, we propose and analyze an efficient implicit–explicit second-order backward
differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems …

A fully self-consistent second order accuracy model for coupling a generalized external
circuit and a one-dimensional bounded electrode-driven plasma was proposed in this …

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 …

We prove that the two-step backward differentiation formula (BDF) method is stable on
arbitrary time grids; while the variable-step three-step backward differentiation formula …

This work establishes-norm stability and convergence for an L2 method on general
nonuniform meshes when applied to the subdiffusion equation. Under mild constraints on …