{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21587"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21587","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Generalized BDF methods applied to Hessenberg form DAEs","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Keiper, Jerry Bruce"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Gear, C.W."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:13:05Z","date_published":"2011-05-07T13:13:05Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Computer Science"],"languages":["eng"],"rights":["Copyright 1989 Keiper, Jerry Bruce"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010913","(UMI)AAI9010913"],"render_values":[{"text":"AAI9010913","href":null,"code":true},{"text":"(UMI)AAI9010913","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21587","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Gear, C.W."]},{"key":"dc:creator","label":"Author","values":["Keiper, Jerry Bruce"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:13:05Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Keiper, Jerry Bruce"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010913","(UMI)AAI9010913","http://hdl.handle.net/2142/21587"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2011-05-07T13:13:05Z (GMT). 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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.","Made available in DSpace on 2011-05-07T13:13:05Z (GMT). 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