Review on Solving 2-D Poisson Problem by Finite and Compact Difference Methods

Finite difference methods (FDM) are a popular class of numerical techniques for solving differential equations this is done by approximating derivatives with finite differences. Compact finite difference schemes enable us to produce more precise results with constrained grid sizes. The idea behind the derivation of the highorder compact scheme is to operate on the differential equations as an auxiliary relation to obtain finite difference approximations for high-order derivatives in the truncation error. In this paper, to generate approximate derivatives using finite differences, we shall discuss Taylor series expansions. For obtaining a more accurate numerical solution we will derive a compact finite difference methods. Finally, we will compare the two methods by solving twodimensional Poisson equation in a rectangular domain.