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An exponential-type integrator for the KdV equation

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Abstract

We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in \(H^1\) for initial data in \(H^3\). Furthermore, we outline the generalization of the presented technique to a second-order method.

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Acknowledgements

K. Schratz gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.

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Authors and Affiliations

  1. Institute of Mathematics, Technical University Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Martina Hofmanová

  2. Fakultät für Mathematik, Karlsruhe Institute of Technology, Englerstr. 2, 76131, Karlsruhe, Germany

    Katharina Schratz

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  1. Martina Hofmanová
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  2. Katharina Schratz
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Correspondence to Katharina Schratz.

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Hofmanová, M., Schratz, K. An exponential-type integrator for the KdV equation. Numer. Math. 136, 1117–1137 (2017). https://doi.org/10.1007/s00211-016-0859-1

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  • DOI: https://doi.org/10.1007/s00211-016-0859-1

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