6.2 Modification of Solution Procedures

 Gauss-Seidel has two advantages over Newton-Raphson in computer

implementations. First, it is easy to implement, as it requires only

iterative solution of the equations. Second, it requires much less

computation per iteration. Because of this, Gauss-Seidel is the first

iterative technique tried by GENIE to solve a set of equations. Using

the methods described in the previous section, the convergence charac-

teristics of the proposed solution procedure are evaluated. If the

analysis indicates that the solution procedure is likely to be conver-

gent, the solution procedure is accepted. Remember that the equations

are, in general, non-linear and thus the solution procedure will be

only locally convergent.

 If the proposed solution procedure is not locally convergent, it

must somehow be modified in an attempt to make it locally convergent.

One modification possible is to choose some equations and variables to

be solved by Newton-Raphson rather than by Gauss-Seidel. Consider the

FVIM in Fig. 6-1 a). Here the incidences are indicated by x's, sinre

the indices themselves are of no particular interest.. Suppose that the

solution procedure represented by a) is found not to be convergent. It

might be modified by moving the functions g and Y and the variables y

and z into a Newton-Raphson solution block. The function d would be

assigned the variable v as an output. The solution procedure would then

be reflected by the FVIM in Fig. 6-1 b). The diagonal blocks are then

solved in Gauss-Seidel fashion. That is, the i-L .ton-RFapihsn variables

are torn, the (1,1) block is solved by Gauss-Seidel, and the calculated

variables are substituted into the Newton-Raphson functions, which are