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
denote variables and functions in
(for some fixed dimension
), and sans-serif upper-case letters
denote
real-valued matrices.