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ANALYTICAL METHODS FOR TRANSPORT EQUATIONS IN SIMILARITY FORM

We present a novel approach for deriving analytical solutions to transport equations expressedin similarity variables. We apply a fixed-point iteration procedure to these transformedequations by formally solving for the highest derivative term and then integrating to obtainan expression for the solution in terms of a previous estimate. We are able to analyticallyobtain the Lipschitz condition for this iteration procedure and, from this (via requirements forconvergence given by the contraction mapping principle), deduce a range of values for the outerlimit of the solution domain, for which the fixed-point iteration is guaranteed to converge.

Identiferoai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:gradschool_theses-1460
Date01 January 2007
CreatorsTiwari, Abhishek
PublisherUKnowledge
Source SetsUniversity of Kentucky
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceUniversity of Kentucky Master's Theses

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