In this paper we illustrate a novel approach for studying the asymptotic behaviour of the solutions of linear difference equations with variable coefficients. In particular, we deal with the zero-stability of the 3-step BDF-method on grids with variable stepsize for the numerical solution of IVPs for ODEs. Our approach is based on the theory of the spectral radius of a family of matrices and yields almost optimal results, which give a slight improvement to the best results already known from the literature. The success got on the chosen example suggests that our approach has a good potential for more general and harder stability analyses of numerical methods.

On the zero-stability of variable stepsize multistep methods: the spectral radius approach

GUGLIELMI N;
2001

Abstract

In this paper we illustrate a novel approach for studying the asymptotic behaviour of the solutions of linear difference equations with variable coefficients. In particular, we deal with the zero-stability of the 3-step BDF-method on grids with variable stepsize for the numerical solution of IVPs for ODEs. Our approach is based on the theory of the spectral radius of a family of matrices and yields almost optimal results, which give a slight improvement to the best results already known from the literature. The success got on the chosen example suggests that our approach has a good potential for more general and harder stability analyses of numerical methods.
BDF formulae, variable stepsize, zero-stability, joint spectral radius
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/302
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