A new BDF-type scheme is proposed for the numerical integration of the system of ordinary differential equations that arises in the Method of Lines solution of time-dependent partial differential equations. This system is usually stiff, so it is desirable for the numerical method to solve it to have good properties concerning stability. The method proposed in this article is almost L-stable and...

Abstract. Asymptotic properties of solutions of general linear differential-algebraic equations (DAE’s) and those of their numerical counterparts are discussed. New results on the asymptotic stability in the sense of Lyapunov as well as on contractive index-2 DAE’s are given. The behaviour of BDF, IRK, and PIRK applied to such systems is investigated. In particular, we clarify the significance ...

I describe an adaptive h-reenement method for solving systems of parabolic partial diierential equations in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for...

The initial-value problem for a first-order evolution equation is discretised in time by means of the two-step backward differentiation formula (BDF) on a variable time grid. The evolution equation is governed by a monotone and coercive potential operator. On a suitable sequence of time grids, the piecewise constant interpolation and a piecewise linear prolongation of the time discrete solution...

Aims. We investigate the ionizing properties of pair bright Ly α emitting galaxies BDF521 and BDF2195 at z = 7.012 in order to constrain their contribution formation Bremer Deep Field (BDF) ‘reionized bubble’ which they have been shown reside. Methods. obtain constraints on four UV emission lines (the CIV λ 1548 doublet, HeII 1640, OIII] 1660 CIII] 1909 doublet) from deep VLT X-shooter observat...

Background One of the important activities that physicians - particularly general practitioners - perform is prescribing. It occurs in most health care facilities and especially in primary health care (PHC) settings. Objectives This study aims to determine what types of prescribing errors are made in PHC at Bahrain Defence Force (BDF) Hospital, and how common they are. Methods This was a re...

BACKGROUND Outpatient parenteral antimicrobial therapy (OPAT) is the administration of intravenous antimicrobial therapy to patients in an outpatient setting. It may be used for patients who have infections that require parenteral treatment but who are otherwise stable enough to not require admission as inpatients. OBJECTIVE We aimed to review the treatment of patients with acute tonsillophar...

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 using a scalar auxiliary (SAV) approach. Comparing the traditional SAV approach (Shen et al. in J Comput Phys 353:407–416, 2018), only use first-order method to approximate variable. This treatment does not affec...

The Feynman-Kac equation governs the distribution of statistical observable — functional, having wide applications in almost all disciplines. After overcoming some challenges from time-space coupled nonlocal operator and possible low regularity this paper develops high-order fully discrete scheme for backward fractional by using difference formulas (BDF) convolution quadrature time, finite elem...

Ct values, the concentration of free chlorine multiplied by time of contact with virus, were determined for free-chlorine inactivation experiments carried out with chloroform-extracted (dispersed) and non-chloroform-extracted (aggregated) feline calicivirus (FCV), adenovirus type 40 (AD40), and polio virus type 1 (PV-1). Experiments were carried out with high and low pH and temperature conditio...