Practical symplectic partitioned Runge--Kutta and Runge--Kutta--Nyström methods

  • Authors:

  • S. Blanes;P. C. Moan

  • Affiliations:

  • Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK;Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

Quantified Score

Hi-index 7.32

Visualization

Abstract

We present new symmetric fourth and sixth-order symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods. We studied compositions using several extra stages, optimising the efficiency. An effective error, Ef, is defined and an extensive search is carried out using the extra parameters. The new methods have smaller values of Ef than other methods found in the literature. When applied to several examples they perform up to two orders of magnitude better than previously known method, which is in very good agreement with the values of Ef.