In this pivotal chapter we give an introduction to a number of mathematical and standardised techniques to analyse partial differential equations before approximating them by the finite difference method. The main technique is to transform a PDE on an unbounded domain to a modified PDE on a bounded domain. Having done that, we apply the Fichera theory to determine what the behaviour will be on the boundary.

The Fichera theory does not seem to be widely known in the computational finance community at the moment of writing