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

Zdzislaw Jackiewicz; A. Marthinsen; B. Owren

doi:10.1023/A:1016645730465

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

Zdzislaw Jackiewicz, A. Marthinsen, B. Owren

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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
DOIs	https://doi.org/10.1023/A:1016645730465
State	Published - 2000

Keywords

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

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1023/A:1016645730465

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title = "Construction of Runge-Kutta methods of Crouch-Grossman type of high order",

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.",

keywords = "Geometric integration, Least squares minimization, Order conditions, Rigid frames, Runge-Kutta methods",

author = "Zdzislaw Jackiewicz and A. Marthinsen and B. Owren",

note = "Funding Information: ∗The work of this author was partially supported by the National Science Foundation under grant NSF DMS-9971164.",

year = "2000",

doi = "10.1023/A:1016645730465",

language = "English (US)",

volume = "13",

pages = "405--415",

journal = "Advances in Computational Mathematics",

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

AU - Jackiewicz, Zdzislaw

AU - Marthinsen, A.

AU - Owren, B.

N1 - Funding Information: ∗The work of this author was partially supported by the National Science Foundation under grant NSF DMS-9971164.

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

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DO - 10.1023/A:1016645730465

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EP - 415

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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