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Error analysis of implicit Runge–Kutta methods for quasilinear hyperbolic evolution equations

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Abstract

We establish error bounds of implicit Runge–Kutta methods for a class of quasilinear hyperbolic evolution equations including certain Maxwell and wave equations on full space or with Dirichlet boundary conditions. Our assumptions cover algebraically stable and coercive schemes such as Gauß and Radau collocation methods. We work in a refinement of the analytical setting of Kato’s well-posedness theory.

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Authors and Affiliations

  1. Department of Mathematics, Karlsruhe Institute of Technology, 76149, Karlsruhe, Germany

    Marlis Hochbruck & Roland Schnaubelt

  2. AVL AST d.o.o. Croatia, 10020, Zagreb, Croatia

    Tomislav Pažur

Authors
  1. Marlis Hochbruck
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  2. Tomislav Pažur
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  3. Roland Schnaubelt
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Correspondence to Marlis Hochbruck.

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This work was supported by the Deutsche Forschungsgemeinschaft (DFG) via CRC 1173.

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Hochbruck, M., Pažur, T. & Schnaubelt, R. Error analysis of implicit Runge–Kutta methods for quasilinear hyperbolic evolution equations. Numer. Math. 138, 557–579 (2018). https://doi.org/10.1007/s00211-017-0914-6

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  • DOI: https://doi.org/10.1007/s00211-017-0914-6

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