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.
| Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:gradschool_theses-1460 |
| Date | 01 January 2007 |
| Creators | Tiwari, Abhishek |
| Publisher | UKnowledge |
| Source Sets | University of Kentucky |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | University of Kentucky Master's Theses |
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