ABSTRACT
The finite difference method (FDM) was first developed by A. Thom in the 1920s under the title "the method of squares" to solve nonlinear hydrodynamic equations. The finite difference techniques are based upon approximations which permit replacing differential equations by finite difference equations. These finite difference approximations are algebraic in form; they relate the value of the dependent variable at a point in the solution region to the values at some neighboring points. Before finding the finite difference solutions to specific PDEs, this chapter looks at how one constructs finite difference approximations from a given differential equation. The application of the finite difference method to elliptic PDEs often leads to a large system of algebraic equations, and their solution is a major problem in itself. Two commonly used methods of solving the system of equations are band matrix and iterative methods.
