On Review of the Consistency and Stability Results for Linear Multistep Iteration Methods in the Solution of Uncoupled Systems of Initial Value Differential Problems

Abstract

The linear multistep method is a numerical method for solving the initial value problem, x’ = f(t,x); x(t0) = x0. A typical linear multistep method is given by X x hf; k1nkjnjjnj+=−+=+=+jkjk010. If βk ≠ 0, then, the method is called implicit. Otherwise, it is called an explicit method. Several methods abound for deriving linear multistep methods; however, in this work, we center on analysis of the convergence and stability of the linear multistep methods. To this effect, we discussed extensively on the convergence, relative, and weak stability theories while preliminarily, we discussed the truncation errors of the linear multistep methods and consistency conditions for the convergence of the linear multistep methods.