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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.


Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000062620
ISSN: 2365-662X
URN: 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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