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 …

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 …

In this paper, we propose and analyze a linear second-order numerical method for solving
the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is …

A novel discrete gradient structure of the variable-step fractional BDF2 formula
approximating the Caputo fractional derivative of order is constructed by a local-nonlocal …

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 …

In this paper, we consider a class of k-order (3≤ k≤ 5) backward differentiation formulas
(BDF-k) for the molecular beam epitaxial (MBE) model without slope selection. Convex …

In this paper, the binary fluid-surfactant phase field model on evolving surfaces is presented
and numerically studied for interfacial sciences. Based on the evolving surface finite element …

In this article, a fast numerical method is developed for solving the FitzHugh-Nagumo (FHN)
model by combining two-grid finite element (TGFE) algorithm in space with a linearized …

This work is concerned with numerical analysis of the variable-step time filtered backward
Euler scheme (see eg DeCaria in SIAM J Sci Comput 43 (3): A2130–A2160, 2021) for linear …

In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2
(WSBDF2) methods for the anisotropic Cahn–Hilliard (CH) model, combining the scalar …