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Stability analysis of phase fitted variational integrators
Author(s) -
Kosmas Odysseas,
Leyendecker Sigrid
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410413
Subject(s) - integrator , eigenvalues and eigenvectors , variational integrator , stability (learning theory) , phase (matter) , work (physics) , mathematics , matrix (chemical analysis) , numerical analysis , numerical stability , control theory (sociology) , mathematical analysis , computer science , physics , materials science , thermodynamics , control (management) , quantum mechanics , machine learning , composite material , computer network , bandwidth (computing) , artificial intelligence
In the present work, we discuss the benefits, limitations and restrictions for the high order phase fitted variational integrators, derived specifically for the numerical integration of systems with oscillatory solutions. To do that, we study linear stability properties of these methods using the eigenvalues of the amplification matrix. The obtained stability region verifies their good behavior, when used for the numerical solution of highly oscillatory problems. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)