THE DYNAMICS OF RUNGE–KUTTA METHODS

1992/09/01 by Julyan H. E. Cartwright, JULYAN H. E. CARTWRIGHT, ORESTE PIRO +1 · 4 citations
Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · doi:10.1142/s0218127492000641

Abstract

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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