ABSTRACT
A numerical solution of a differential equation consists of a set of numbers from which the distribution of the dependent variable ϕ can be constructed. This chapter encounters the discretization concept in another context. The continuum calculation domain has been discretized. It is this systematic discretization of space and of the dependent variables that makes it possible to replace the governing differential equations with simple algebraic equations, which can be solved with relative ease. A discretization equation is an algebraic relation connecting the values of ϕ for a group of grid points. Such an equation is derived from the differential equation governing ϕ and thus expresses the same physical information as the differential equation. For a given differential equation, the possible discretization equations are by no means unique, although all types of discretization equations are, in the limit of a very large number of grid points, expected to give the same solution.
