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Title:An Algorithm for the Detection and Integration of Highly Oscillatory Ordinary Differential Equations Using a Generalized Unified Modified Divided Difference Representation
Author(s):Gallivan, Kyle Andrew
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Computer Science
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.
Issue Date:1983
Description:117 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983.
Other Identifier(s):(UMI)AAI8409929
Date Available in IDEALS:2014-12-15
Date Deposited:1983

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