K-Step Block Implicit Adams Method for Approximate Solution of Initial Value Problems using Eulerian Polynomial

Abstract

This paper constructs and applied a class of k-step Block Implicit Adams Method (BIAM) for  the integration of first order initial value problems in which the Eulerian polynomial is employed as the basis function .The BIAM for the initial value problems is constructed via multistep collocation techniques and applied in block structure as simultaneous numerical integration which makes it self-starting. An analysis of BIAM shows that the proposed method is zero stable, consistent, convergence and A-stable. Application of the BIAM on some standard ordinary differential problems revealed that BIAM is efficient and a good approximating scheme.