Abstract: In the perturbation finite difference (PFD) method both the differentials and non- differential terms in the differential equation studied are discretized. High accuracy and high resolution difference schemes are obtained with the differentials being approximated by the direct differences (i.e., second-order-accurate center difference and first-order-accurate upwind difference). PFD method includes the perturbation exact numerical solution (PENS) scheme for locally lin- earized differential equation and t...