Introduction to non-standard finite-difference modelling

Peter Malcolm Manning, Gary F. Margrave

This report introduces some of the principles and uses of non-standard finite-difference modelling. It begins with a review of the elements of finite-differences, and how continuous derivatives are replaced with differences, and incorporated into a 'scheme'. It shows examples of scheme selection by testing. Finally, it demonstrates some more advanced strategies of standard finite-differencing for stability or higher accuracy. Then the nonstandard ideas are introduced. A set of standard finite-differences is compared with their equivalent 'exact' finite-differences. It finishes with some examples where exact difference forms are incorporated into non-standard schemes.