Construction of Runge-Kutta methods of Crouch-Grossman type of high order

Zdzislaw Jackiewicz, A. Marthinsen, B. Owren

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


An approach is described to the numerical solution of order conditions for Runge-Kutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg-Marquardt algorithm. Methods of order four and five are constructed and numerical experiments are presented which confirm that the derived methods have the expected order of accuracy.

Original languageEnglish (US)
Pages (from-to)405-415
Number of pages11
JournalAdvances in Computational Mathematics
Issue number4
StatePublished - 2000


  • Geometric integration
  • Least squares minimization
  • Order conditions
  • Rigid frames
  • Runge-Kutta methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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