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Zbl 0867.65038
Butcher, J.C.; Wanner, G.
Runge-Kutta methods: Some historical notes. (English)
[J] Appl. Numer. Math. 22, No.1-3, 113-151 (1996). ISSN 0168-9274

We cite from the abstract: ``$\ldots$ This centenary history of Runge-Kutta methods contains an appreciation of the early work of Runge, Heun, Kutta, and Nyström and a survey of some significant developments of these methods over the last hundred years. In particular, the order conditions $\ldots$ will be outlined, $\ldots$ the introduction and practical implementation of implicit Runge-Kutta methods, the use of linear and nonlinear stability analysis $\ldots$ the theory and applications of the composition of methods $\ldots$ Runge-Kutta methods for Hamiltonian systems $\ldots$''. Of great interest are also the comments on an early article of Coriolis (1837), and the picture of the historically first order star.
[E.Hairer (Genève)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
01A55 Mathematics in the 19th century
65-03 Historical (numerical analysis)
01A60 Mathematics in the 20th century
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: historical survey; Runge-Kutta methods; order conditions; stability; Hamiltonian systems; order star

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Zentralblatt MATH Berlin [Germany]