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Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems Read chapter Read first chapter

2018 | OriginalPaper | Chapter

8. A Compact Tri-Colored Tree Theory for General ERKN Methods

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

This chapter develops a compact tri-colored rooted-tree theory for the order conditions for general ERKN methods. The bottleneck of the original tri-colored rooted-tree theory is the existence of numerous redundant trees. This chapter first introduces the extended elementary differential mappings. Then, the new compact tri-colored rooted tree theory is established based on a subset of the original tri-colored rooted-tree set. This new theory makes all redundant trees no longer appear, and hence the order conditions of ERKN methods for general multi-frequency and multidimensional second-order oscillatory systems are greatly simplified.

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previous chapter Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems
next chapter An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations
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Metadata
Title
A Compact Tri-Colored Tree Theory for General ERKN Methods
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_8

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