Formulation of Some Linear Multistep Schemes for Solving First Order Initial Value Problems Using Canonical Polynomials as Basis Functions

摘要

In this study, we shall present the derivation and application of some linear multistep methods in solving initial value problems for first order Ordinary Differential Equations (ODES) using canonical polynomials as basic functions. By interpolating and collocating at some selected points, some important classes of linear multistep methods were generated. The methods derived shall be compared with well known Adams Moulton method of the same order. Some numerical examples were given to illustrate the effectiveness of these methods.