## Date of Award

5-1995

## Document Type

Thesis

## Degree Name

Master of Science

## Department

Department of Mathematics and Statistics

## First Advisor

Michael Stoecker, PhD

## Abstract

This study is an extension of Ng's previous work in which goal programming was used to determine an approximate solution to a boundary value problem. This approach follows the same basic approach developed by Ng in which the method of collocation was recast as a compromise programming model. Hence, instead of solving a system of simultaneous nonlinear equations, one seeks a compromise solution which minimizes (in a weighted residual sense) a vector norm of the differential equation residuals. A difference in this approach is that it makes use of a genetic algorithm as the optimizing engine as opposed to the pattern search used by Ng. The model developed in this approach also consists of a modification to the generalized compromise programming model by eliminating the need for deviation variables. As a result, this model is a simplification in that the number of decision variables is completely independent of the number of collocation points. This technique is very robust in that it has been shown to produce good results on a variety of problems. The results of four example problems compare favorably with those of Ng and other solution techniques.

## AFIT Designator

AFIT-ENC-GOR-95J-01

## DTIC Accession Number

ADA297406

## Recommended Citation

Zornick, John L., "A Robust Method of Solving Nonlinear Boundary Value Problems via Modified Compromise Programming" (1995). *Theses and Dissertations*. 6466.

https://scholar.afit.edu/etd/6466