On strong stability preserving time discretization methods. (English) Zbl 1074.65095

Higueras, Inmaculada

J. Sci. Comput. 21, No. 2, 193-223 (2004).

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.

Reviewer: Laura-Iulia Aniţa (Iaşi)

MSC:

65L20	Stability and convergence of numerical methods for ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

strong-stability preserving; monotonicity; Runge-Kutta methods; comparison of methods; initial value problem