The numerical-analysis literature usually refers to this as the “initial value problem”. Unfortunately, in a relativity context this terminology often causes confusion with the “initial data problem” of solving the ADM constraint equations. I use the term “time-integration problem for ODEs” to (try to) avoid this confusion. In this appendix, sans-serif lower-case letters abc...z denote variables and functions in ℜn (for some fixed dimension n), and sans-serif upper-case letters ABC ...Z denote n× n real-valued matrices.