Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?

Authors:
G. Vanden Berghe;M. Van Daele;H. Vande Vyver
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Universiteit-Gent, Krijgslaan 281-S9, B9000 Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Universiteit-Gent, Krijgslaan 281-S9, B9000 Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Universiteit-Gent, Krijgslaan 281-S9, B9000 Gent, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

Two different classes of exponential fitted Runge-Kutta collocation methods are considered: methods with fixed points and methods with frequency-dependent points. For both cases we have obtained extensions of the classical two-stage Gauss, RadauIIA and LobattoIIIA methods. Numerical examples reveal important differences between both approaches.