Abstract
This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant.
We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity.
General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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Spijker, M.N. A note on contractivity in the numerical solution of initial value problems. BIT 27, 424–437 (1987). https://doi.org/10.1007/BF01933735
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DOI: https://doi.org/10.1007/BF01933735