A rapid method for approximating invariant manifolds of differential equations

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dc.contributor.authorTang, Shouchun (Terry)
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorRoussel, Marc R.
dc.date.accessioned2007-07-13T17:58:22Z
dc.date.available2007-07-13T17:58:22Z
dc.date.issued2006
dc.degree.levelMasters
dc.descriptionvii, 61 leaves ; 29 cm.en
dc.description.abstractThe Intrinsic Low-Dimensional Manifold (ILDM) has been adopted as an approximation to the slow manifold representing the long-term evolution of a non-linear chemical system. The computation of the slow manifold simplifies the model without sacrificing accuracy because the trajectories are rapidly attracted to it. The ILDM has been shown to be a highly accurate approximation to the manifold when the curvature of the manifold is not too large. An efficient method of calculating an approximation to the slow manifold which may be equivalent to the ILDM is presented. This method, called Functional Equation Truncation (FET). is based on the assumption that the local curvature of the manifold is negligible, resulting in a locally linearized system. This system takes the form of a set of algebraic equations which can be solved for given values of the independent variables. Two-dimensional and three-dimensional models are used to test this method. The approximations to onedimensional slow manifolds computed by FET are quite close to the corresponding ILDMs and those for two-dimensional ones seem to differ from their ILDM counterparts.en
dc.identifier.urihttps://hdl.handle.net/10133/356
dc.language.isoen_USen
dc.publisherLethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006en
dc.publisher.departmentDepartment of Chemistry and Biochemistryen
dc.publisher.facultyArts and Scienceen
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en
dc.subjectDissertations, Academicen
dc.subjectManifolds (Mathematics)en
dc.subjectLow-dimensional topologyen
dc.subjectDifferential equationsen
dc.titleA rapid method for approximating invariant manifolds of differential equationsen
dc.typeThesisen
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