On the Review of Linear Multistep Methods as Fixed Point Iterative Methods in the Solution of a Coupled System of Initial Value Differential Problem

Abstract

The linear multi-step method, xxhfknkjkjnjjkjjnj+=−+=+=+0101;, a numerical method for solving the initial value problem xftxxtx'=()()=,,00 is hereby analytically reviewed and observations show that the linear multistep method is a typical Picard’s fixed point iterative formula with a differential operator endowed with some numerical reformulations instead of the usual integral operator as in the traditional Picard’s method. The study also shows that any given linear multistep iterative method will be convergent to a fixed point if and only if it is consistent and stable. This was adequately illustrated with an example as is contained in section three of this work.