ABSTRACT
Finite difference equations are obtained by substituting the finite difference approximations of the individual exact partial derivatives into the PDE. Two types of FDEs can be developed, depending on the base point chosen for the FDAs. If grid point (i, n) is chosen as the base point of the FDAs, then J;n+ I appears only in the finite difference approximation of];. In that case, the FDE can be solved directly for J;n+ I. Such FDEs are called explicit FDEs. However, if grid point (i, n + I) is chosen as the base point of the FDAs, thenJ;n+1 appears in the finite difference approxima!ions of both]; andlxx' andJ;~jl and J;~jl appear in the finite difference approximation offxx. In that case,J;"+1 cannot be solved for directly, sinceJ;"+1 depends onJ;~jl andJ;~jl, which are also unknown. Such FDEs are called implicit FDEs.
