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. The iterative methods are generally used to solve a large system of simultaneous equations. An iterative method for solving equations is one in which a first approximation is used to calculate a second approximation, which in turn is used to calculate a third approximation, and so on. There are three sources of errors that are nearly unavoidable in numerical solution of physical problems: modeling errors, truncation (or discretization) errors, and roundoff errors. Each of these error types will affect accuracy and therefore degrade the solution.
