A new derivation of continuous collocation multistep methods using power series as basis function

Abstract

Some derivations of Continuous Linear Multistep Methods are given in this paper. The paper provides the use of both collocation and interpolation techniques to obtain the schemes. Rather than using Chebyshev polynomials as basis function as it was always done in the past, we introduced the use of direct form of power series as an alternative to the derivation of these schemes. Multistep Methods have over the years been one of the most popular and acceptable methods for generating solutions to initial value problems of Ordinary Differential Equations.