Abstract: The main purpose of this paper is to present some convergence results of a class of Parallel Multivalue Hybrid Methods (PMHMs) for semi-explicit index-2 differential-algebraic equations. Some numerical examples confirm our theoretical results and show that the computed orders of the 2-step 2-order PMHM (PMHM2) and the 3-step 3-order PMHM (PMHM3) are higher than the corresponding theor...

Quasi-linear parabolic equations are discretised in time by fully implicit backward difference formulae (BDF) as well as by implicit–explicit and linearly implicit BDF methods up to order 5. Under appropriate stability conditions for the various methods considered, we establish optimal order a priori error bounds by energy estimates, which become applicable via the Nevanlinna-Odeh multiplier te...

We analyze stability properties of BDF methods of order up to 5 for linear parabolic equations as well as of implicit–explicit BDF methods for nonlinear parabolic equations by energy techniques; time dependent norms play also a key role in the analysis.

Abstract. We derive optimal order, residual-based a posteriori error estimates for time discretizations by the two–step BDF method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Euler scheme. Our a posteriori error estimates are of...

For backward differentiation formulae (BDF) applied to gradient flows of semiconvex functions, quadratic stability implies the existence a Lyapunov functional. We compute maximum time step which can be derived from for 3-step BDF method (BDF3). Applications asymptotic behaviour sequences generated by BDF3 scheme are given.

The basal transcription factor TFIID consists of the TATA-binding protein (TBP) and TBP-associated factors (TAFs). Yeast Taf67 is homologous to mammalian TAF(II)55. Using a yeast two-hybrid screen to identify proteins that interact with Taf67, we isolated Bromodomain factor 1 (Bdf1) and its homolog (Bdf2). The Bdf proteins are genetically redundant, as cells are inviable without at least one of...

A linear parabolic differential equation on a moving surface is discretized in space by evolving surface finite elements and in time by backward difference formulas (BDF). Using results from Dahlquist’s G-stability theory and Nevanlinna & Odeh’s multiplier technique together with properties of the spatial semi-discretization, stability of the full discretization is proven for the BDF methods up...

We report a novel strategy for the regulation of charge transport through single molecule junctions via the combination of external stimuli of electrode potential, internal modulation of molecular structures, and optimization of anchoring groups. We have designed redox-active benzodifuran (BDF) compounds as functional electronic units to fabricate metal-molecule-metal (m-M-m) junction devices b...

The paper presents a new result for the existence and uniqueness of solutions of the system of nonlinear algebraic equations obtained from the application of the BDF methods to stii initial value problems in ordinary diierential equations. Expressed in terms of the local truncation error, starting errors in the BDF and contractivity properties of the diierential equation, the result is used to ...

Balanced diet fed (BDF) rats injected with Salmonella typhi 'H' antigen showed an initial suppression of an immunomodulatory bone marrow cytokine Frl (BM-Frl) followed by stimulation, whereas the cytokine secretory pattern showed only stimulation in immunized vitamin B complex malnourished rats. This nutritional-dependent differential response of a bone marrow cytokine to antigen is similar to ...