A numerical method for systems of ordinary differential equations

<p>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.</p> <p>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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Year

1977

Author dc:creator

• Raefsky, Arthur

Contributors dc:contributor

• Rao Vemuri
• James Geer
• Andrew Barto

• Differential equations

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/384

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1390