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

Error analysis of implicit Runge–Kutta methods for quasilinear hyperbolic evolution equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Deutschland
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0029-599X
eISSN
0945-3245
D.O.I.
10.1007/s00211-017-0914-6
Publisher site
See Article on Publisher Site

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.

Journal

Numerische MathematikSpringer Journals

Published: Aug 28, 2017

References

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