A systematic way of extending a general fixed-stepsize multistep formula to a minimum storage variable-stepsize formula has been discovered that encompasses fixed-coefficient (interpolatory), variable-coefficient (variable step), and fixed leading coefficient as special cases. In particular, it is shown that the " interpolatory" stepsize changing technique of Nordsieck leads to a truly variable...

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.

The availability of central reference information as thesauri is critical for correct intellectual access to distributed databases, in particular to digital collections in international networks. There is a continuous raise in interest in thesauri, and several thesaurus management systems have appeared on the market. The issue, how to integrate effectively such central resources into a multitud...

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...

We consider a simplified model of an unconfined one-dimensional detonation problem, giving a brief survey of the history of the problem and of its numerical solution. This problem with its mathematical features is typical of those solved commercially by ICI plc, and the specific values used for the chemical constants in the example are typical of those of interest. Unfortunately, not all obviou...

A new formula called 2-point diagonally implicit super class of BBDF with two off-step points (2ODISBBDF) for solving stiff IVPs is formulated. The method approximates two solutions with two off-step points simultaneously at each iteration. By varying a parameter ρ ∈ (–1,1) in the formula, different sets of formulae can be generated. A specific choice of 3 4 ρ = is made and it was shown that th...

Finite difference approximations of dynamical systems modelled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.

Previous studies of the stability of the second-order backward differentiation formula have concluded that stability is possible only if restrictions are placed on the stepsize ratios, for example, limiting the ratio to some value less than 1 + fi. However, actual implementations of the BDFs differ from the usual theoretical models of such methods; in particular, practical codes use scaled deri...