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Zbl 1196.65117
Van De Vyver, Hans
Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems. (English)
[J] Comput. Phys. Commun. 173, No. 3, 115-130 (2005). ISSN 0010-4655

Summary: In this paper we make an extensive analysis of the imaginary stability of many explicit Runge-Kutta methods with variable coefficients for oscillatory problems. The Runge-Kutta methods considered are based on several construction procedures such as exponential fitting, phase-fitting or dissipative-fitting (the latter two techniques can be combined). Two-dimensional regions of imaginary stability for the first-order test model are obtained. These regions are a generalization of the imaginary stability intervals of classical Runge-Kutta methods. To have an idea of the numerical performance of the methods we have also made a phase-lag and dissipation analysis.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: numerical methods for odes; Runge-Kutta methods; exponential Fitting; phase-Fitting; stability analysis; phase-lag analysis

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