I need to find some masters-level exercises about numerical methods for solving ODEs. Are there any good references?
Since nobody else has mentioned them, I will recommend Solving Ordinary Differential Equations (volumes I and II) by Hairer, Nørsett, and Wanner.
If you do not mind a "self-reference" there is "Differential Equations, Mechanics, and Computation", published by AMS and written by me and my son Bob Palais. See the associated website at:
The second half of the book (the part written by Bob) is a quite complete treatment of numerical methods for solving ODEs, and has lots of exercises.
One good book is Ascher and Petzold (Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations).
Another good book is Numerical Solution of Ordinary Differential Equations by Shampine.
Trefethen's book Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations is also great (and free online).
Differential Equations and Boundary Value Problems: Computing and Modeling, 4/E Authors: C. Henry Edwards and David E. Penney.
There are different reviews of this book http://www.amazon.com/Differential-Equations-Computing-Modeling-Edition/dp/0136004385