KIT | KIT-Bibliothek | Impressum | Datenschutz

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.


Volltext §
DOI: 10.5445/IR/1000062620
Cover der Publikation
Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-626203
KITopen-ID: 1000062620
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 ; 2016/33
Schlagwörter quasi-linear evolution equations, symmetric hyperbolic systems, dispersive equations, implicit midpoint rule, algebraic stability, implicit Runge–Kutta method, coercivity, energy estimates, error bounds
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page