Derivation and Analysis of Block Implicit Hybrid Backward Differentiation Formulae (HBDF) for Stiff Problems.

Abstract

The Hybrid Backward Differentiation Formula (HBDF) for the case k = 3 was reformulated into continuous form using the idea of multistep collocation. The continuous form was evaluated at some grid and off grid points which gave rise to discrete schemes employed as block methods for direct solution of first order Ordinary Differential Equation y^' = f(x; y). The requirement of a starting value and the overlap of solution model which are associated with conventional Linear Multistep Methods were eliminated by this approach. A convergence analysis of the derived hybrid schemes to establish their effec- tiveness and reliability is presented. Numerical example carried out on stiff problem further substantiates their performance.