Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type
Numerical Analysis
2017-04-12 v2
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.
Keywords
Cite
@article{arxiv.1611.08176,
title = {Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type},
author = {Balázs Kovács and Christian Lubich},
journal= {arXiv preprint arXiv:1611.08176},
year = {2017}
}