On strong stability preserving time discretization methods
This paper concerns the following initial value problem \[ u'(t)=f(t,u(t)),\;t\geq t_0,\quad u(t_0)=u_0 \] such that its solution satisfies a monotonicity property: \[ \| u(t)\|\leq \| u(t_0)\|,\quad \forall t\geq t_0, \] for a given norm \(\|\cdot\|\). The monotonicity for Runge-Kutta methods is investigated. A review of some known results is done. These results are compared with those obtained in the strong stability preserving (SSP) context.
scientific article; zbMATH DE number 2153853