Stability analysis of the BDF slowest first multirate methods This paper deals with the stability analysis of the BDF Slowest first multirate time-integration methods which are applied to the transient analysis of circuit models. From an asymptotic analysis it appears that these methods are indeed stable if the subsystems are stable and weakly coupled. Index 1. Introduction 1.1. Partition of th...

There is increasing interest in single nucleotide polymorphism (SNP) typing since they can be used as markers to identify the genes that underlie complex diseases and to realize the full potential of pharmacogenomics in analyzing variable response to drugs. Among the different methodologies for SNP genotyping, the homogenous assay is more amenable than the heterogeneous one. In this article, we...

The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for ...

AIMS The aim of this study was to isolate a thermotolerant micro-organism that produces polyhydroxyalkanoates (PHAs) composed of medium-chain-length (mcl) HA units from a biodiesel fuel (BDF) by-product as a carbon source. METHODS AND RESULTS We successfully isolated a thermotolerant micro-organism, strain SG4502, capable to accumulate mcl-PHA from a BDF by-product as a carbon source at a cul...

We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while variable-step three-step scheme if almost all adjacent step ratios are less than 2.553. These results relax severe mesh restrictions in literature and provide a new understanding of BDF methods. Our main tools include discrete orthogonal convolution kernels an elliptic type matrix n...

Two di erent time-stepping schemes are investigated for a phaseeld model of solidi cation of a pure material. A rst order accurate semiexplicit scheme which is computationally cheap per time step is compared to a more accurate fully implicit BDF-discretization. The implementation of fast Poisson and Newton-GMRES solvers are discussed in some detail. Convergence rates are experimentally validate...

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 ...