On the Parametric Instability Caused by Step Size Variation in Runge-Kutta-Nystr\"om Methods
Numerical Analysis
2012-09-25 v1 Numerical Analysis
Abstract
The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\"om (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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Cite
@article{arxiv.1209.5173,
title = {On the Parametric Instability Caused by Step Size Variation in Runge-Kutta-Nystr\"om Methods},
author = {Robert Piché},
journal= {arXiv preprint arXiv:1209.5173},
year = {2012}
}
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11 pages