Algorithms for generating solution procedures for non-indexed

equation sets have been programmed for use on digital computers by

Cunningham (1972, 1973). The package of computer programs is called

GENDER, for General Engineering Design Routines. The GENDER system is

designed to provide an integrated computer program package for auto-

matically generating solution procedures.

 The goal of this dissertation is to provide to the GENDER system

a means of generating solution procedures for sets of indexed equations.

The computer programs developed to do this are called the GENIE system,

GENIE being an acronym for GENDER with Indexed Equations. Chapters 2

to 4 detail modifications both to existing algorithms and to the means

of representing the set of equations which allow an automatic derivation

of a solution procedure.

 The way that the data are represented within the computer storage,

i.e., the data structure, has a profound effect on both the total

storage required and on the time required to execute an algorithm.

Chapter 5, along with Appendix A, discuss the various data structures

used.

 Although the algorithms developed in Chapters 2 to 4 allow a

 solution procedure based on structural considerations to be derived,

 there is, unfortunately, no guarantee that the solution procedure will

 converge unless the system of equations fully precedence orders, i.e.,

 is completely acyclic. It is desirable to base a solution procedure

 not only on structural considerations, but also on numerical consider-

 ations. Chapter 6 discusses some of the relevant numerical consider-

 ations and gives some insight into the prediction of convergence

 properties.