Thesis (Ph. D.)--Oregon State University, 1974. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Revision of the author's thesis, Bern, 1960. / Bibliography: p. 345-355.

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We derive and analyse two families of multistep collocation methods for periodic initial-value problems of the form y" = f(x, y); y((^x)o) = yo, y(^1)(xo) = zo involving ordinary differential equations of second order in which the first derivative does not appear explicitly. A survey of recent results and proposed numerical methods is given in chapter 2. Chapter 3 is devoted to the analysis of a family of implicit Chebyshev methods proposed by Panovsky k Richardson. We show that for each non-negative integer r, there are two methods of order 2r from this family which possess non-vanishing intervals of periodicity. The equivalence of these methods with one-step collocation methods is also established, and these methods are shown to be neither P-stable nor symplectic. In chapters 4 and 5, two families of multistep collocation methods are derived, and their order and stability properties are investigated. A detailed analysis of the two-step symmetric methods from each class is also given. The multistep Runge-Kutta-Nystrom methods of chapter 4 are found to be difficult to analyse, and the specific examples considered are found to perform poorly in the areas of both accuracy and stability. By contrast, the two-step symmetric hybrid methods of chapter 5 are shown to have excellent stability properties, in particular we show that all two-step 27V-point methods of this type possess non-vanishing intervals of periodicity, and we give conditions under which these methods are almost P-stable. P-stable and efficient methods from this family are obtained and demonstrated in numerical experiments. A simple, cheap and effective error estimator for these methods is also given.

Regensburg, Universiẗat, Diss., 1995.

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Propagation of radiation in a waveguides is theoretically described by Maxwell&amp / #8217 / s equations. The gradient of refractive index and an influence on the waveguide by a superstrate requires a numerical solution of the differential equation. Iterative methods such as the Runge-Kutta approaches are used to calculate the effective refractive index in the waveguide depending on the superstrate&amp / #8217 / s and the waveguide&amp / #8217 / s local refractive indices. In this study,the refractive indices, and the model fields of the TE00 modes are calculated. The calculated fields of the 00 TE modes give information about the propagation of the light in the waveguide. Also, the precision of the Runge-Kutta aproaches has been tested. The advantages and disadvantages of the Runge-Kutta aproaches are discussed.

Thèse de doctorat : Mécanique. Mécanique des Fluides : Strasbourg 1 : 2008. / Thèse soutenue sur un ensemble de travaux. Titre provenant de l'écran-titre. Notes bibliogr.