The steady state and transient methods used in SINDA/G® are discussed in this paper. The basic finite difference method is explained and derived from the heat equation. Explanations of the various control constants and rule of thumb settings are presented. Various numerical errors such as truncation, discretization and round-off are discussed. A speed comparison of the routines is presented in the form of bar charts. Finally, guidelines are presented for selecting a routine for a particular type of problem.