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Gallivan, Kyle Andrew 2014-12-15T19:25:29Z 2014-12-15T19:25:29Z 10000-01-01 1983 1983 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). No. of bitstreams: 1 8409929.pdf: 3565872 bytes, checksum: 4919e257f6ae239eda6895d208218769 (MD5) Previous issue date: 1983 Embargo set by: Seth Robbins for item 69690 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 117 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983. http://hdl.handle.net/2142/69524 (UMI)AAI8409929 Computer Science An Algorithm for the Detection and Integration of Highly Oscillatory Ordinary Differential Equations Using a Generalized Unified Modified Divided Difference Representation text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.