Two problems are studied. First, the analytic continuation of the real periodic solutions of van der Pol's equation to complex values of the damping parameter $\varepsilon$ are discussed. This continuation shows the existence of an infinite family of singular complex periodic solutions associated with values of $\varepsilon$ lying on two curves $\Gamma$ and $\bar\Gamma$ (see Figure 8) located symmetrically in the $\varepsilon$-plane. These singular solutions are found to cause the existence of the moving singularities of the Poincare-Lindstedt series for the real limit cycle which were developed at great length by Andersen and Geer (7), and were analyzed, using Pade approximants, by Dadfar et al. (10). A numerical method for the computation of these singular solutions is described. In addition, an asymptotic description of them for large values of $\vert\varepsilon\vert$ is obtained using the method of matched asymptotic expansions. Our results suggest that the existence of the complex singular solutions may, in general, play an important role in the utility of computer-generated perturbation expansions at moderate or large values of the perturbation parameter. / Our second study involves a model, due to Lagerstrom, of the steady flow of a viscous incompressible fluid past an object in (m + 1) dimensions. The model is a nonlinear boundary-value problem in the range $\varepsilon \leq x $ 0 and $m >$ 0. Our results suggest that a similar iteration may be an effective method of approximation of viscous flows at moderate Reynolds numbers. / Source: Dissertation Abstracts International, Volume: 51-07, Section: B, page: 3416. / Major Professor: Christopher Hunter. / Thesis (Ph.D.)--The Florida State University, 1990.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_78282 |
| Contributors | Tajdari, Mohammad Sina., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 143 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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