DERIVATION AND ANALYSIS OF BLOCK IMPLICIT HYBRID BACKWARD DIFFERENTIATION FORMULAE FOR STIFF PROBLEMS

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 wasevaluated at some grid and of grid points, which gave rise to discrete schemes employed as block methods for direct solution of the first-order ordinary differential equation y0 = f(x; y). Therequirement of a starting value and the overlap of the solution model, which are associated with conventional linear multistep methods, were eliminated by this approach. A convergenceAn analysis of the derived hybrid schemes to establish their effectiveness and reliability is presented. A numerical example carried out on the still problem further substantiates their performance.