ABSTRACT
This chapter presents discretization of partial differential equations by Taylor series expansion and by control volumes and discusses the types of errors involved in the discretization process and during the solution of the resulting system of algebraic equations. A formal basis for developing finite difference approximation of derivatives is through the use of Taylor series expansion. In the alternative control volume approach, the finite difference equations are developed by constraining the partial differential equation to a finite control volume and conserving the specific physical quantity such as mass, momentum, or energy over this control volume. In the solution of differential equations with finite differences, a variety of schemes are available for the discretization of derivatives and the solution of the resulting system of algebraic equations. The discretization error increases with increasing mesh size, while the round-off error decreases with increasing mesh size.
