Alcune osservazioni su una classe di metodi lineari multistep A-stabili

Abstract

In this note we observe a decreasing property of $||F_n||²_G$ along the numerical solution of the autonomous differential system $\dot{y}=f(y)$ 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 $F_n=(f^T(y_n),f^T(y_{n+1}),...f^T(y_{n+k-1}))^T$ and G is a symmetric positive definite matrix of order k. We study also a particular subclass of linear multistep A-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.