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...

The type-section of the Blackwater Draw Formation (BDF) consists a series five paleosol horizons developed on eolian deposits and an overlying surficial soil. Previous work has shown that magnetic properties (e.g., χ, ARM, IRM) as function depth in this type-section, display both magnetically enhanced depleted signals for different paleosols. To better understand mineralogy responsible these va...

This study compares self-reported sexual behaviors from a retrospective survey and a prospective diary among Botswana Defence Force (BDF) personnel. One hundred sixty-one male participants, aged 18-30, completed two weekly prospective diaries and a retrospective survey querying them about behaviors reported during the same time frame as the diaries. Most reported behaviors were similar between ...

There are three important steps in the proof the BDF theorem for essentially normal operators having essential spectrum X ⊆ C. (1) Ext(X) has a neutral element. (2) Ext(X) is a group (i.e., has inverses). (3) Ext(X) depends only on the homotopy class of X. In this lecture we will exhibit the neutral element of Ext(X) and describe the generalization of that result to noncommutative C∗-algebras (...

The subject of the paper is the numerical simulation of the interaction of twodimensional compressible viscous flow and a vibrating airfoil. The airfoil is considered as a solid body with two degrees of freedom, moving in the vertical direction and rotating around an elastic axis. The numerical simulation consists of the solution of the Navier-Stokes system by the space discontinuous Galerkin m...

A new algorithm for numerical sensitivity analysis of ordinary differential equations (ODEs) is presented. The underlying ODE solver belongs to the Runge–Kutta family. The algorithm calculates sensitivities with respect to problem parameters and initial conditions, exploiting the special structure of the sensitivity equations. A key feature is the reuse of information already computed for the s...

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precisi...

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial proble...

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the f...