ABSTRACT
This chapter presents the finite difference procedures, and the mathematical and numerical concepts needed to use such procedures. Four methods for constructing a nite difference approximation are introduced, namely, the direct approximation, Taylor series, polynomial representation, and control volume approaches. In the direct approximation approach, partial derivatives are directly replaced by ratios of discrete differences. A Taylor series approach is needed to obtain the mathematical form of truncation error. The polynomial representation method is particularly convenient for deriving nite difference approximations for grid points that are nonuniformly distributed. The control volume method is particularly useful for the numerical imposition of practical boundary conditions that are generally more involved than Dirichlet conditions. The control volume method is the preferred method for obtaining the nite difference equations for the boundary conditions. The chapter provides an introduction to de nitions associated with the solution of linear algebraic equations.
