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


Abstract


In this note we observe a decreasing property of ||F<sub>n</sub>||<sup>2</sup><sub>G</sub> 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(Error rendering LaTeX formula) 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.

DOI Code: 10.1285/i15900932v1n2p261

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