Higher order time stepping for second order hyperbolic problems and optimal CFL conditions

J. Charles Gilbert; Patrick Joly

doi:10.1007/978-1-4020-8758-5_4

Higher order time stepping for second order hyperbolic problems and optimal CFL conditions

J. Charles Gilbert
, Patrick Joly

INRIA Rocquencourt

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases. We propose variants of these schemes constructed to optimize the CFL condition. The corresponding optimization problem is analyzed in detail and the analysis results in a specific numerical algorithm. The corresponding results are quite promising and suggest various conjectures.

Original language	English
Title of host publication	Partial Differential Equations
Subtitle of host publication	Modeling and Numerical Simulation
Editors	Roland Glowinski, Pekka Neittaanmäki
Publisher	Springer
Pages	67-93
Number of pages	27
ISBN (Print)	9781402087578
DOIs	https://doi.org/10.1007/978-1-4020-8758-5_4
Publication status	Published - 1 Jan 2008
Externally published	Yes
Event	International Conference on Partial Differential Equations: Modeling and Numerical Simulation, 2005 - Helsinki, Finland Duration: 1 Jan 2005 → …

Publication series

Name	Computational Methods in Applied Sciences
Volume	16
ISSN (Print)	1871-3033

Conference

Conference	International Conference on Partial Differential Equations: Modeling and Numerical Simulation, 2005
Country/Territory	Finland
City	Helsinki
Period	1/01/05 → …

Access to Document

10.1007/978-1-4020-8758-5_4

Cite this

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title = "Higher order time stepping for second order hyperbolic problems and optimal CFL conditions",

abstract = "We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases. We propose variants of these schemes constructed to optimize the CFL condition. The corresponding optimization problem is analyzed in detail and the analysis results in a specific numerical algorithm. The corresponding results are quite promising and suggest various conjectures.",

author = "Gilbert, \{J. Charles\} and Patrick Joly",

year = "2008",

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doi = "10.1007/978-1-4020-8758-5\_4",

language = "English",

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series = "Computational Methods in Applied Sciences",

publisher = "Springer",

pages = "67--93",

editor = "Roland Glowinski and Pekka Neittaanm{\"a}ki",

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note = "International Conference on Partial Differential Equations: Modeling and Numerical Simulation, 2005 ; Conference date: 01-01-2005",

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Gilbert, JC & Joly, P 2008, Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. in R Glowinski & P Neittaanmäki (eds), Partial Differential Equations: Modeling and Numerical Simulation. Computational Methods in Applied Sciences, vol. 16, Springer, pp. 67-93, International Conference on Partial Differential Equations: Modeling and Numerical Simulation, 2005, Helsinki, Finland, 1/01/05. https://doi.org/10.1007/978-1-4020-8758-5_4

Higher order time stepping for second order hyperbolic problems and optimal CFL conditions. / Gilbert, J. Charles; Joly, Patrick.
Partial Differential Equations: Modeling and Numerical Simulation. ed. / Roland Glowinski; Pekka Neittaanmäki. Springer, 2008. p. 67-93 (Computational Methods in Applied Sciences; Vol. 16).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Higher order time stepping for second order hyperbolic problems and optimal CFL conditions

AU - Gilbert, J. Charles

AU - Joly, Patrick

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases. We propose variants of these schemes constructed to optimize the CFL condition. The corresponding optimization problem is analyzed in detail and the analysis results in a specific numerical algorithm. The corresponding results are quite promising and suggest various conjectures.

AB - We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases. We propose variants of these schemes constructed to optimize the CFL condition. The corresponding optimization problem is analyzed in detail and the analysis results in a specific numerical algorithm. The corresponding results are quite promising and suggest various conjectures.

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T2 - International Conference on Partial Differential Equations: Modeling and Numerical Simulation, 2005

Y2 - 1 January 2005

ER -

Higher order time stepping for second order hyperbolic problems and optimal CFL conditions

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