These notes contain an extended summary of a lecture given at the 20th Biennial Conference on Numerical Analysis, Dundee, 2003. This review is largely based on material from [7,8], where additional results and a more precise presentation can be found.

Multistep, Runge-Kutta and extrapolation methods (msc 65L06), Finite difference methods (msc 65M06), Method of lines (msc 65M20)
Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Multiscale Dynamics

Hundsdorfer, W, & Ruuth, S.J. (2003). Monotonicity for time discretizations. Modelling, Analysis and Simulation [MAS]. CWI.