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Runge‐Kutta‐Nyström Methods with Maximized Stability Domain for Problems in Strutural Mechanics
Author(s) -
Lunk Christoph
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410326
Subject(s) - runge–kutta methods , smoothness , spurious relationship , stability (learning theory) , domain (mathematical analysis) , mathematics , dimension (graph theory) , focus (optics) , frequency domain , mathematical analysis , numerical analysis , computer science , physics , pure mathematics , optics , statistics , machine learning
Structural dynamics applications feature a particular type of second order stiff equations, often in combination with low smoothness of the right hand side, large dimension and non‐linear force terms. As alternative to implicit schemes, explicit Runge‐Kutta‐Nyström methods are analysed, with focus on low order and maximized stability domain since spurious high frequency oscillations need not be resolved. It turns out that it is possible to construct methods with a stability domain that stretches up to hω = 2 s on the imaginary axis where h is the stepsize, ω the largest frequency in the system, and s the stage number. Some numerical examples show the competitiveness of the proposed methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)