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Runge-Kutta methods: Some historical notes. (English) Zbl 0867.65038

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.
Reviewer: E.Hairer (Genève)

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
01A55 History of mathematics in the 19th century
65-03 History of numerical analysis
01A60 History of mathematics in the 20th century
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems

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