Hi again,
A colleague just pointed out this article [1] where they use different discretization schemes. I believe that your question is sufficiently broad (try "nonuniform finite differences" as a search term) that this will have been addressed in other publications too.
Happy Kwanting,
Joe
[1]: http://scitation.aip.org/content/aip/journal/jap/68/8/10.1063/1.346245