Document Type

Dissertation

Date of Award

1977

Keywords

Differential equations

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering

First Advisor

Rao Vemuri

Second Advisor

James Geer

Third Advisor

Andrew Barto

Abstract

This dissertation demonstrates the utility, generality and simplicity of a new computational method of solving systems of ordinary differential equations. The central idea of this new method revolves around our ability to generate a numerical approximation of the general solution of systems of linear differential equations. The idea of obtaining a numerical approximation to the general solution leads to changes in the traditional approaches for solving boundary value problems. The method is extended to solve nonlinear initial and boundary value problems by using it in conjunction with quasilinearization. An important contribution of this dissertation is in the application of the proposed method to the estimation of unknown parameters in a dynamical system.

The question of solving singular perturbation problems for ordinary differential equations, and problems characterized by large positive eigenvalues are also treated. Towards this end the method developed in this dissertation is used in conjunction with the modified quasilinearization algorithm, with a grid refinement algorithm introduced into the solution procedure. The ability to find a general solution to systems of ordinary differential equations, also puts in a new light the question of solving partial differential equations via the method of lines. Illustrative examples are presented to demonstrate this point.

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