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arXiv · 1611.08176

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

Balázs Kovács·Christian Lubich
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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 fluid 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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Balázs Kovács, Christian Lubich. 2016-11-24. Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type. https://arxiv.org/abs/1611.08176

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