Block Implicit Hybrid Linear Multistep Methods for Solution of Ordinary Differential Equations

Abstract

The idea of multistep collocation is employed to reformulate the Hybrid Backward Differentiation Formula (HBDF) for cases k=4 and 6 into continous forms which were evaluated at some interpolation and collocation points.This gives rise to discrete schemes that are combined to form the efficient block method for the solution of Ordinary Differential Equations. The requirement of starting values and the overlap of solution model which are associated with conventional Linear Multistep Methods are eliminated by this approach. A convergence analysis of the derived hybrid schemes is presented to establish their effectiveness and reliability. Numerical examples carried out further substantiates their convergence.