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Runge-Kutta methods for orthogonal and isospectral flows

✍ Scribed by M.P. Calvo; A. Iserles; A. Zanna

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
541 KB
Volume
22
Category
Article
ISSN
0168-9274

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✦ Synopsis

Orthogonal and isospectral flows occur in many applications and they possess important invariants. However, a naive application of Runge-Kutta methods is bound to render these invariants incorrectly. In this paper we describe how to retain relevant invariants with Runge-Kutta methods or, alternatively, incur an error in the rendition of the invariants which is significantly smaller than the overall numerical error.

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A simple characterisation exists for the class of real-valued, autonomous, matrix ODEs where an orthogonal initial condition implies orthogonality of the solution for all time. Here we present first and second order numerical methods for which the property of orthogonality-preservation is always car