Summary
In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
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van Veldhuizen, M. OnD-stability andB-stability. Numer. Math. 42, 349–357 (1983). https://doi.org/10.1007/BF01389579
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DOI: https://doi.org/10.1007/BF01389579