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

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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.

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Acknowledgments

The authors are sincerely thankful to two anonymous reviewers for their valuable comments.

Funding

The research is supported in part by the Alexander von Humboldt Foundation, by NSF of Shandong Province (Outstanding Youth Foundation, no. ZR2017JL003), and by NSFC (no.11671200).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Bin Wang & Xinyuan Wu

  2. Mathematisches Institut, University of Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Bin Wang

  3. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Xinyuan Wu

Authors
  1. Bin Wang
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  2. Xinyuan Wu
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Correspondence to Xinyuan Wu.

Additional information

Dedicated to John Butcher on the occasion of his 85th birthday.

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Wang, B., Wu, X. Global error bounds of one-stage extended RKN integrators for semilinear wave equations. Numer Algor 81, 1203–1218 (2019). https://doi.org/10.1007/s11075-018-0585-0

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  • DOI: https://doi.org/10.1007/s11075-018-0585-0

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