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Numerische Mathematik

, Volume 138, Issue 2, pp 365–388 | Cite as

Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type

  • Balázs Kovács
  • Christian LubichEmail author
Article

Abstract

Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where the solution is sufficiently regular, we show stability and optimal-order convergence of the linearly implicit and fully implicit midpoint rules and of higher-order implicit Runge–Kutta methods that are algebraically stable and coercive, such as the collocation methods at Gauss nodes.

Mathematics Subject Classification

65M12 

Notes

Acknowledgements

This work was supported by Deutsche Forschungsgemeinschaft, SFB 1173. We thank two anonymous referees for constructive comments on a previous version.

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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany

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