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2018 | OriginalPaper | Chapter

1. Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems

Authors : Xinyuan Wu, Bin Wang

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

Publisher: Springer Singapore

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Abstract

In recent decades, the numerical simulation for nonlinear oscillators has received much attention and a large number of integrators for oscillatory problems have been developed. In this chapter, based on the continuous finite element approach, we propose and analyse new energy-preserving functionally-fitted, in particular, trigonometrically-fitted methods of an arbitrarily high order for solving oscillatory nonlinear Hamiltonian systems with a fixed frequency. In order to implement these new methods in an accessable and efficient style, they are formulated as a class of continuous-stage Runge–Kutta methods. The numerical results demonstrate the remarkable accuracy and efficiency of the new methods compared with the existing high-order energy-preserving methods in the literature.

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next chapter Exponential Average-Vector-Field Integrator for Conservative or Dissipative Systems
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Metadata
Title
Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems
Authors
Xinyuan Wu
Bin Wang
Copyright Year
2018
Publisher
Springer Singapore
Book
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 Year: 2018

DOI
https://doi.org/10.1007/978-981-10-9004-2_1

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