block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of th...

The production of fatty acid methyl esters (FAMEs) from waste activated bleaching earth (ABE) discarded by the crude oil refining industry using lipase from Candida cylindracea was investigated in a 50-L pilot plant. Diesel oil or kerosene was used as an organic solvent for the transesterification of triglycerides embedded in the waste ABE. When 1% (w/w) lipase was added to waste ABE, the FAME ...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHTα method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 ...

Implicit integration methods have contributed to large performance enhancements in the field of simulation of particle-system mechanical models. While Backward Euler and BDF-2 methods are now widely used for cloth simulation applications, the Implicit Midpoint method is often overlooked, because of its poor stability properties. It is however as simple to implement as Backward Euler, and offers...

We have developed a structured adaptive mesh refinement (SAMR) method for parabolic partial differential equation (PDE) systems. Solutions are calculated using the finite-difference or finite-volume method in space and backward differentiation formula (BDF) integration in time. The combination of SAMR in space and BDF in time is designed for problems where the fine-scale profile of sharp fronts...

Veratridine modification of Na current was examined in single dissociated ventricular myocytes from late-fetal rats. Extracellularly applied veratridine reduced peak Na current and induced a noninactivating current during the depolarizing pulse and an inward tail current that decayed exponentially (tau = 226 ms) after repolarization. The effect was quantitated as tail current amplitude, Itail (...

We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In...

The time discretisation of the initial-value problem for a first-order evolution equation by the two-step backward differentiation formula (BDF) on a uniform grid is analysed. The evolution equation is governed by a time-dependent monotone operator that might be perturbed by a time-dependent strongly continuous operator. Well-posedness of the numerical scheme, a priori estimates, convergence of...

ABSTRACT We show herein that the population of star-forming galaxies in Bremer Deep Field (BDF) has enough ionizing power to form two large ionized bubbles could be process merging into a one with volume 14 000 cMpc3. The sources identified BDF have been completed set expected low-luminosity at z ∼ 7. estimated number photons per second produced by different BDF. This compared would required io...