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The Dynamics of Runge--Kutta Methods

Julyan H. E. Cartwright & Oreste Piro gif
School of Mathematical Sciences
Queen Mary and Westfield College
University of London
Mile End Road
London E1 4NS

[Int. J. Bifurcation and Chaos, 2, 427-449, 1992]


The first step in investigating the dynamics of a continuous-time system described by an ordinary differential equation is to integrate to obtain trajectories. In this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge--Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.

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Julyan Cartwright
Wed Sep 27 17:21:22 MET 1995