The stability of rational approximations of cosine functions on Hilbert spaces

Authors:
I. Alonso-Mallo;B. Cano;M. J. Moreta
Affiliations:
Departamento de Matemática Aplicada, Universidad de Valladolid, C/ Doctor Mergelina s.n., 47011 Valladolid, Spain;Departamento de Matemática Aplicada, Universidad de Valladolid, C/ Doctor Mergelina s.n., 47011 Valladolid, Spain;Departamento Fundamentos del Análisis Económico I, Facultad de Ciencias Económicas y Empresariales, Universidad Complutense de Madrid, Campus de Somosaguas, Pozuelo de Alarcón, ...
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

In this paper, it is proved the stability of rational methods for the time discretization of abstract well-posed second order in time problems where the differential operator generates a cosine function. The particular case of operators associated to a sesquilinear form is studied in detail. These rational methods are suitable for these problems and they can be defined, for example, by using Runge-Kutta-Nystrom methods.