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.