Methods for accurately determining solutions of degenerate boundary va
lue problems are described. Nonlinear problems are first approximated
by sequences of linear problems. A finite difference procedure which i
ncorporates the effect of the degeneracy in the matrix of the linear d
iscretized system of equations is developed. The simple tridiagonal st
ructure of the matrix allows fast, accurate calculations to be perform
ed with quite modest computer support. The results are readily improve
d using Richardson extrapolation.