Global error bounds of one-stage extended RKN integrators for semilinear wave equations

Bin Wang; Xinyuan Wu

doi:10.1007/s11075-018-0585-0

Global error bounds of one-stage extended RKN integrators for semilinear wave equations

Bin Wang
, Xinyuan Wu

Qufu Normal University
University of Tübingen
Nanjing University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

This paper analyzes global error bounds of one-stage explicit extended Runge–Kutta–Nyström integrators for semilinear wave equations. The analysis is presented by using spatial semidiscretizations with periodic boundary conditions. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.

Original language	English
Pages (from-to)	1203-1218
Number of pages	16
Journal	Numerical Algorithms
Volume	81
Issue number	4
DOIs	https://doi.org/10.1007/s11075-018-0585-0
State	Published - 1 Aug 2019
Externally published	Yes

Keywords

Error bounds
Extended Runge–Kutta–Nyström integrators
Semilinear wave equations
Trigonometric integrators

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10.1007/s11075-018-0585-0

Cite this

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title = "Global error bounds of one-stage extended RKN integrators for semilinear wave equations",

abstract = "This paper analyzes global error bounds of one-stage explicit extended Runge–Kutta–Nystr{\"o}m integrators for semilinear wave equations. The analysis is presented by using spatial semidiscretizations with periodic boundary conditions. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.",

keywords = "Error bounds, Extended Runge–Kutta–Nystr{\"o}m integrators, Semilinear wave equations, Trigonometric integrators",

author = "Bin Wang and Xinyuan Wu",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

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N2 - This paper analyzes global error bounds of one-stage explicit extended Runge–Kutta–Nyström integrators for semilinear wave equations. The analysis is presented by using spatial semidiscretizations with periodic boundary conditions. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.

AB - This paper analyzes global error bounds of one-stage explicit extended Runge–Kutta–Nyström integrators for semilinear wave equations. The analysis is presented by using spatial semidiscretizations with periodic boundary conditions. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.

KW - Error bounds

KW - Extended Runge–Kutta–Nyström integrators

KW - Semilinear wave equations

KW - Trigonometric integrators

UR - https://www.scopus.com/pages/publications/85052289525

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DO - 10.1007/s11075-018-0585-0

M3 - 文章

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JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 4

ER -

Global error bounds of one-stage extended RKN integrators for semilinear wave equations

Abstract

Keywords

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