### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 405-415 |

Number of pages | 11 |

Journal | Advances in Computational Mathematics |

Volume | 13 |

Issue number | 4 |

State | Published - 2000 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics

### Cite this

*Advances in Computational Mathematics*,

*13*(4), 405-415.

**Construction of Runge-Kutta methods of Crouch-Grossman type of high order.** / Jackiewicz, Zdzislaw; Marthinsen, A.; Owren, B.

Research output: Contribution to journal › Article

*Advances in Computational Mathematics*, vol. 13, no. 4, pp. 405-415.

}

TY - JOUR

T1 - Construction of Runge-Kutta methods of Crouch-Grossman type of high order

AU - Jackiewicz, Zdzislaw

AU - Marthinsen, A.

AU - Owren, B.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Geometric integration

KW - Least squares minimization

KW - Order conditions

KW - Rigid frames

KW - Runge-Kutta methods

UR - http://www.scopus.com/inward/record.url?scp=0034563116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034563116&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034563116

VL - 13

SP - 405

EP - 415

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

IS - 4

ER -