Introduzione

Abstract

EnIn this note we observe a decreasing property of ${\big \Vert {Fn} \big \Vert} _{G}2$ along the numerical solution of the autonomous differential system $y'=f(x)$ which satisfies a monotonicity condition;such a solution is obtained by means of a class of linear k-step A-stable methods and we have set $Fn = ({fT}({yn}), {fT}(y_{n+1}), ... , {fT}(y_{n+k-1}))T$ and G is a symmetric positive definite matrix of order k. We study also a particular subclass of linear multistep G-stable methods of maximum order,in which the matrix G is actually constructed.The associated Lyapunov function ensures the stability of the set of equilibrium points