Next steps

We use Runge-Kutta methods as a class to represent what are also called single-step or one-step methods. A gentle introduction to these and other kinds of IVP methods can be found in Atkinson and Han [Atk89]. More advanced introductions are given in Corless and Fillon [CF13] and Iserles [Ise96]. The most definitive reference is by Hairer et al. [HNorsettW08].

A dated but still interesting article about the built-in functions for solving initial value problems in MATLAB is by Shampine [SR97]. Methods for a more general type of problem known as differential–algebraic equations are covered in Brenan et al. [BCP96].

Interesting history of IVP methods can be found at the SIAM website, where C. W. Gear gives both an oral history and an article reprinted from [Nas90]).