Alcune osservazioni su una classe di metodi lineari multistep A-stabili
Abstract
In this note we observe a decreasing property of
along the numerical solution of the autonomous differential system
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.
![||F<sub>n</sub>||<sup>2</sup><sub>G</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8c07049d7776ad2095d21580a1ec5444.png)
![\dot{y}=f(y)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/b076ec2bd1cc8df9b4b4fda93de70287.png)
DOI Code:
10.1285/i15900932v1n2p261
Full Text: PDF