{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69524"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69524","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"An Algorithm for the Detection and Integration of Highly Oscillatory Ordinary Differential Equations Using a Generalized Unified Modified Divided Difference Representation","abstract":"This thesis describes an algorithm which automatically integrates systems of ordinary differential equations which have highly oscillatory solutions. Natural variable step derivations of the Generalized Adams and Generalized BDF methods are presented. An efficient numerical algorithm for the evaluation of the local period of an oscillation is presented along with a corresponding algorithm which detects behavior that indicates the system may be amenable to solution by the generalized methods. A code, which implements the algorithm and exploits the overwhelming similarity between the generalized methods and conventional integration methods, is discussed along with some numerical results.","abstract_html":"This thesis describes an algorithm which automatically integrates systems of ordinary differential equations which have highly oscillatory solutions. Natural variable step derivations of the Generalized Adams and Generalized BDF methods are presented. An efficient numerical algorithm for the evaluation of the local period of an oscillation is presented along with a corresponding algorithm which detects behavior that indicates the system may be amenable to solution by the generalized methods. A code, which implements the algorithm and exploits the overwhelming similarity between the generalized methods and conventional integration methods, is discussed along with some numerical results.","abstract_has_math":false,"creators":["Gallivan, Kyle Andrew"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:25:29Z","date_published":"2014-12-15T19:25:29Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Computer Science"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8409929"],"render_values":[{"text":"(UMI)AAI8409929","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69524","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gallivan, Kyle Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:25:29Z","10000-01-01","1983"]},{"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":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69524","(UMI)AAI8409929"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis describes an algorithm which automatically integrates systems of ordinary differential equations which have highly oscillatory solutions. Natural variable step derivations of the Generalized Adams and Generalized BDF methods are presented. An efficient numerical algorithm for the evaluation of the local period of an oscillation is presented along with a corresponding algorithm which detects behavior that indicates the system may be amenable to solution by the generalized methods. A code, which implements the algorithm and exploits the overwhelming similarity between the generalized methods and conventional integration methods, is discussed along with some numerical results.","Made available in DSpace on 2014-12-15T19:25:29Z (GMT). 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Natural variable step derivations of the Generalized Adams and Generalized BDF methods are presented. An efficient numerical algorithm for the evaluation of the local period of an oscillation is presented along with a corresponding algorithm which detects behavior that indicates the system may be amenable to solution by the generalized methods. A code, which implements the algorithm and exploits the overwhelming similarity between the generalized methods and conventional integration methods, is discussed along with some numerical results.","Made available in DSpace on 2014-12-15T19:25:29Z (GMT). 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