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2018 | OriginalPaper | Buchkapitel

7. Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems

verfasst von : Xinyuan Wu, Bin Wang

Erschienen in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Verlag: Springer Singapore

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Abstract

This chapter presents a class of trigonometric collocation methods based on Lagrange basis polynomials for solving multi-frequency and multidimensional oscillatory systems \(q^{\prime \prime }(t)+Mq(t)=f\big (q(t)\big )\). The properties of the collocation methods are investigated in detail. It is shown that the convergence condition of these methods is independent of \(\left\| M\right\| \), which is crucial for solving multi-frequency oscillatory systems.

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Vorheriges Kapitel The Construction of Arbitrary Order ERKN Integrators via Group Theory

Nächstes Kapitel A Compact Tri-Colored Tree Theory for General ERKN Methods

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Titel: Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems
verfasst von: Xinyuan Wu
Bin Wang
Verlag: Springer Singapore
Buch: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
Print ISBN: 978-981-10-9003-5

Electronic ISBN: 978-981-10-9004-2

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-981-10-9004-2_7

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