Finite difference methods for ordinary boundary value problems

Finite difference methods have been shown to be extremely effective in the accurate and efficient solution of very general nonlinear two point boundary value problems. As with all practical numerical methods their development is tied very closely to the theoretical understanding of the procedures in question. Not surprisingly then there has been much current work on the theory of difference methods for two point problems. We shall recapitulate some of this theory here and also discuss some of the practical aspects in developing standard computer codes for such problems