Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations

Hongyu LIU; Kai ZHANG

doi:10.1093/imanum/dri042

Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations

Hongyu LIU^*, Kai ZHANG

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

17 Citations (Scopus)

Abstract

The non-linear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge-Kutta methods and multi-symplectic partitioned Runge-Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.

Original language	English
Pages (from-to)	252-271
Journal	IMA Journal of Numerical Analysis
Volume	26
Issue number	2
Online published	1 Apr 2006
DOIs	https://doi.org/10.1093/imanum/dri042
Publication status	Published - Apr 2006
Externally published	Yes

Research Keywords

Hamiltonian PDEs
multi-symplectic
non-linear wave equations
partitioned Runge-Kutta method
Runge-Kutta method
stability analysis

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title = "Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations",

abstract = "The non-linear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge-Kutta methods and multi-symplectic partitioned Runge-Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.",

keywords = "Hamiltonian PDEs, multi-symplectic, non-linear wave equations, partitioned Runge-Kutta method, Runge-Kutta method, stability analysis",

author = "Hongyu LIU and Kai ZHANG",

year = "2006",

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doi = "10.1093/imanum/dri042",

language = "English",

volume = "26",

pages = "252--271",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

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TY - JOUR

T1 - Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations

AU - LIU, Hongyu

AU - ZHANG, Kai

PY - 2006/4

Y1 - 2006/4

N2 - The non-linear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge-Kutta methods and multi-symplectic partitioned Runge-Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.

AB - The non-linear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge-Kutta methods and multi-symplectic partitioned Runge-Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.

KW - Hamiltonian PDEs

KW - multi-symplectic

KW - non-linear wave equations

KW - partitioned Runge-Kutta method

KW - Runge-Kutta method

KW - stability analysis

UR - http://www.scopus.com/inward/record.url?scp=33645743266&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33645743266&origin=recordpage

U2 - 10.1093/imanum/dri042

DO - 10.1093/imanum/dri042

M3 - RGC 21 - Publication in refereed journal

SN - 0272-4979

VL - 26

SP - 252

EP - 271

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 2

ER -

Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations

Abstract

Research Keywords

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