Abstract
The first analysis of instability phenomena and step size restrictions for hyperbolic equations was made in the famous paper of Courant, Friedrichs & Lewy (1928). Later, many authors undertook a stability analysis, very often independently, in order to explain the phenomena encountered in the foregoing section. An early and beautiful paper on this subject is Guillou & Lago (1961).
... werden wir bei dem Anfangswertproblem hyperbolischer Gleichungen erkennen, dass die Konvergenz allgemein nur dann vorhanden ist, wenn die Verhältnisse der Gittermaschen in verschiedenen Richtungen gewissen Ungleichungen genügen.
(Courant, Friedrichs & Lewy 1928)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). Stability Analysis for Explicit RK Methods. 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_2
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DOI: https://doi.org/10.1007/978-3-642-05221-7_2
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