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On the parametric instability caused by step size variation in Runge-Kutta-Nyström methods

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Original languageEnglish
Place of PublicationTampere
PublisherTampere University of Technology
Number of pages13
ISBN (Electronic)978-952-15-2804-0
ISBN (Print)952-15-0021-2
Publication statusPublished - 1998
Publication typeD4 Published development or research report or study

Publication series

NameTampere University of Technology, Department of Information Technology, Mathematics Report
PublisherTampere University of Technology
ISSN (Print)1236-956X


The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nyström (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient ODEs are integrated with RKN methods that are based on A-stable Runge-Kutta methods, the solution is nonincreasing in some norm for all positive step sizes, constant or varying. Perturbation methods are used to quantify the critical step sizes associated with parametric instability.

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