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A classification of second order equations via nonlocal transformations.

dc.contributor.advisorGovinder, Keshlan Sathasiva.
dc.contributor.authorEdelstein, R. M.
dc.date.accessioned2011-09-29T09:52:29Z
dc.date.available2011-09-29T09:52:29Z
dc.date.created2000
dc.date.issued2000
dc.descriptionThesis (M.Sc.)-University of Natal, Durban, 2000.en
dc.description.abstractThe study of second order ordinary differential equations is vital given their proliferation in mechanics. The group theoretic approach devised by Lie is one of the most successful techniques available for solving these equations. However, many second order equations cannot be reduced to quadratures due to the lack of a sufficient number of point symmetries. We observe that increasing the order will result in a third order differential equation which, when reduced via an alternate symmetry, may result in a solvable second order equation. Thus the original second order equation can be solved. In this dissertation we will attempt to classify second order differential equations that can be solved in this manner. We also provide the nonlocal transformations between the original second order equations and the new solvable second order equations. Our starting point is third order differential equations. Here we concentrate on those invariant under two- and three-dimensional Lie algebras.en
dc.identifier.urihttp://hdl.handle.net/10413/3694
dc.language.isoenen
dc.subjectDifferential equations--Numerical solutions.en
dc.subjectLie algebras.en
dc.subjectMechanics.en
dc.subjectTransformations (Mathematics)en
dc.subjectTheses--Mathematics.en
dc.titleA classification of second order equations via nonlocal transformations.en
dc.typeThesisen

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