In this paper, stability and error estimates for time discretizations of linear semilinear parabolic equations by the two-step backward differentiation formula (BDF2) method with variable step-sizes are derived. An affirmative answer is provided to question: whether upper bound step-size ratios $l^{\infty }(0,T;H)$ -stability BDF2 identical zero-stability. The }(0,T;V)$ also established under m...

In order to achieve higher computational precision in approximating the first-order derivative of the target point, the 1-step-ahead numerical differentiation formulas are presented. These formulas greatly remedy some intrinsic weaknesses of the backward numerical differentiation formulas, and overcome the limitation of the central numerical differentiation formulas. In addition, a group of for...

In this paper, we propose a full discretization scheme for the instationary thermal-electro-hydrodynamic (TEHD) Boussinesq equations. These equations model dynamics of non-isothermal, dielectric fluid under influence dielectrophoretic (DEP) force. Our combines an H 1 -conformal finite element method spatial with backward differentiation formula (BDF) time stepping. The resulting allows decouple...

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler met...

<p style='text-indent:20px;'>Magnetization dynamics in magnetic materials is often modeled by the Landau-Lifshitz equation, which solved numerically general. In micromagnetics simulations, computational cost relies heavily on time-marching scheme and evaluation of stray field. this work, we propose a new method, dubbed as GSPM-BDF2, combining advantages Gauss-Seidel projection method (GSP...

We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. employ a third order backward differentiation (BDF3) in time implicit treatment of surface diffusion term. The nonlinear term is approximated by explicit extrapolation (EP3) formula. exhibit mild step constraints under which modified energy dissipation law holds. break secon...