Abstract
Order stars, discovered by searching for a better understanding of the stability properties of the Padé approximations to e z (Wanner, Hairer & Nørsett 1978), offered nice and unexpected access to many other results: the “second barrier” of Dahlquist, the Daniel & Moore conjecture, highest possible order with real poles, comparison of stability domains (Jeltsch & Nevanlinna 1981, 1982), order bounds for hyperbolic or parabolic difference schemes (e.g., Iserles & Strang 1983, Iserles & Williamson 1983, Jeltsch 1988).
Mein hochgeehrter Lehrer, der vor wenigen Jahren verstorbene Geheime Hofrath Gauss in Göttingen, pflegte in vertraulichem Gespräche häufig zu äussern, die Mathematik sei weit mehr eine Wissenschaft für das Auge als eine für das Ohr. Was das Auge mit einem Blicke sogleich übersieht ...
(J.F. Encke 1861, publ. in Kronecker’s Werke, Vol. 5, page 391)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). Order Stars. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_4
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DOI: https://doi.org/10.1007/978-3-642-05221-7_4
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