The GENIE system, which is an acronym for GENDER with Indexed

Equations, provides a more efficient means of analyzing sets of indexed

equations. A compact means for representing the structure of indexed

equation sets is presented. This representation allows both existing

and newly developed algorithms to be applied in order to generate a

solution procedure for the indexed equations. An evaluation of the

convergence characteristics of the proposed solution procedure is made,

using order of magnitude estimates of variable values. Should a

proposed solution procedure be found to be non-convergent, means are

provided for modifying it to enhance the likelihood of convergence.

Formulas are presented which allow the estimation of the convergence

properties of the new solution procedure.

 The solution procedures generated are independent of the ranges

on the indices. Conventional methods derive solution procedures for

a particular set of equations. The solution procedures are generated

in the form of F0RTRAN "do-loops," so the index ranges become the

do-loop parameters and can change from application to application.

 Solution procedures have been derived for a typical chemical

engineering problem, a mathematical model of a disti llation column.

Two different problems were solved by the solution procedure. GEN;I

successfully predicted convergence difficulties for or= of the problems

and modified the solution procedure. The modified solution procedure

did solve the problem.