I recommend P. Winternitz, *Group Theory and Numerical Analysis"Analysis, AMS.AMS, 2005.
From Google Books:
The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation.
Also, P.J. Oliver, Applications of Lie Groups to Differential Equations, Springer, 2000.
A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them.
