Numerische Mathematik

, Volume 138, Issue 3, pp 557–579 | Cite as

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

  • Marlis HochbruckEmail author
  • Tomislav Pažur
  • Roland Schnaubelt


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.

Mathematics Subject Classification

Primary: 65M12 65J15 Secondary: 35Q61 35L90 


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  • Marlis Hochbruck
    • 1
    Email author
  • Tomislav Pažur
    • 2
  • Roland Schnaubelt
    • 1
  1. 1.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.AVL AST d.o.o. CroatiaZagrebCroatia

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