## “Simulation of ordinary differential equations on manifolds: some numerical experiments and verifications”Authors: Arne Marthinsen, Hans Munthe-Kaas and Brynjulf Owren,
Affiliation: NTNU
Reference: 1997, Vol 18, No 1, pp. 75-88. |

**Keywords:**Ordinary differential equations, manifolds, numerical analysis, initial value problems

**Abstract:**During the last few years, different approaches for integrating ordinary differential equations on manifolds have been published. In this work, we consider two of these approaches. We present some numerical experiments showing benefits and some pitfalls when using the new methods. To demonstrate how they work, we compare with well known classical methods, e.g. Newmark and Runge-Kutta methods.

PDF (1557 Kb) DOI: 10.4173/mic.1997.1.4

**DOI forward links to this article:**

[1] P. Krysl and L. Endres (2005), doi:10.1002/nme.1272 | |

[2] Arne Marthinsen (1999), doi:10.1137/S0036142998338861 | |

[3] A. Zanna (1999), doi:10.1137/S0036142997326616 | |

[4] Hans Munthe-Kaas (1999), doi:10.1016/S0168-9274(98)00030-0 | |

[5] Phani Kumar V. V. Nukala and William Shelton Jr (2007), doi:10.1002/nme.1874 | |

[6] A. Müller and Z. Terze (2013), doi:10.1016/j.cam.2013.10.039 | |

[7] Stig Faltinsen, Arne Marthinsen and Hans Z. Munthe-Kaas (2001), doi:10.1016/S0168-9274(01)00103-9 | |

[8] Hans Munthe-Kaas (1998), doi:10.1007/BF02510919 | |

[9] L.O. Jay (2004), doi:10.1016/j.camwa.2003.02.013 | |

[10] Andreas Müller and Zdravko Terze (2014), doi:10.1016/j.mechmachtheory.2014.06.014 | |

[11] Zdravko Terze, Andreas Müller and Dario Zlatar (2016), doi:10.1007/s11044-016-9518-7 | |

[12] Andreas Müller and Zdravko Terze (2016), doi:10.1007/s00707-016-1760-9 | |

[13] Charles Curry and Brynjulf Owren (2019), doi:10.1007/s11075-019-00659-0 |

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**BibTeX:**

@article{MIC-1997-1-4,

title={{Simulation of ordinary differential equations on manifolds: some numerical experiments and verifications}},

author={Marthinsen, Arne and Munthe-Kaas, Hans and Owren, Brynjulf},

journal={Modeling, Identification and Control},

volume={18},

number={1},

pages={75--88},

year={1997},

doi={10.4173/mic.1997.1.4},

publisher={Norwegian Society of Automatic Control}

};