CHAPTER 4

 ALGORITHMS FOR DERIVING SOLUTION PROCEDURES
 FOR SETS OF INDEXED EQUATIONS



 The algorithms implemented in the GENDER system for deriving

solution procedures are capable of treating non-indexed equations only.

In deriving a solution procedure GENDER performs the following analyses.

First the acyclic algorithm is applied to determine which parts of the

problem are acyclic and which contain recycle calculations. An output

set assignment is then made. After the outputs are assigned the

precedence ordering is found and the groups of functions and variables

requiring simultaneous solution are identified. The last step is to

choose the tear variables for each group.

 The treatment of indexed equations by GENIE is similar in approach

to that of GENDER. First, the FVIM is analyzed by the acyclic algorithm

to discover the acyclic nature of the set of equations. The decoupling

algorithm is then applied to the set of function and variable types

involved in recycle calculations in an attempt to identify further

acyclic structure. Outputs are next assigned to both function types

and function indices. A precedence ordering of function types is

determined and groups are identified. Finally, the tear variables

within each group are determined by a minimum weighted tearing algo-

rithm.

 The algorithms presented in this chapter perform the particular

analyses necessary for deriving a solution procedure for indexed