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

2018 | OriginalPaper | Chapter

4. Symplectic Exponential Runge–Kutta Methods for Solving Nonlinear 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

Symplecticity is an important property for exponential Runge–Kutta (ERK) methods when the underlying problem \(y'(t)=My(t)+f(y(t))\) is a Hamiltonian system. The main theme of this chapter is to present symplectic exponential Runge–Kutta methods. Using the fundamental analysis of geometric integrators, we first derive and analyse the symplectic conditions for ERK methods. These conditions reduce to the conventional ones when \(M\rightarrow \mathbf {0}\). Furthermore, revised stiff order conditions are proposed and investigated in detail. This chapter is also accompanied by numerical results that demonstrate the potential of the symplectic ERK methods.

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previous chapter Exponential Fourier Collocation Methods for First-Order Differential Equations
next chapter High-Order Symplectic and Symmetric Composition Integrators for Multi-frequency Oscillatory Hamiltonian Systems
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Metadata
Title
Symplectic Exponential Runge–Kutta Methods for Solving Nonlinear 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_4

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