Generalized BDF methods applied to Hessenberg form DAEs

We study the numerical solution of Hessenberg form differential algebraic equations by variable stepsize generalized backward difference formulae (GBDF). GBDF methods of sufficiently high order are shown to converge for problems of index two, three, or four. The proof techniques developed are not sufficiently powerful to show convergence for index five problems. In addition, we perform very high precision numerical experiments on problems of index two, three, four, and five, using the classical six step backward difference formula. The experiments confirm the analysis regarding the error behavior of the index two and three problems, but suggest that the analysis of the index four problem is too pessimistic. It appears from the experiments that index five problems can also be solved by GBDF methods.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Keiper, Jerry Bruce

Contributors dc:contributor

• Gear, C.W.

• Computer Science

Statement dc:rights

• Copyright 1989 Keiper, Jerry Bruce

Language dc:language

eng

Identifier

AAI9010913
(UMI)AAI9010913

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21587