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

Kovács, Balázs; Lubich, Christian

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 uid and wave equations. In the regime where the solution is suffciently 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.

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DOI: 10.5445/IR/1000062620
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Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-626203
KITopen-ID: 1000062620
Verlag KIT, Karlsruhe
Umfang 22 S.
Serie CRC 1173 ; 2016/33
Schlagworte quasi-linear evolution equations, symmetric hyperbolic systems, dispersive equations, implicit midpoint rule, algebraic stability, implicit Runge–Kutta method, coercivity, energy estimates, error bounds
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