Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems

Abstract 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.

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