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Numerical methods have been used to predict the eigenperiods and eigenfunctions of the Earth’s Slichter modes, known as the Slichter triplets. In order to test the validity of our method, we have also computed the frequencies and displacement eigenfunctions of some of the inertial modes of the Earth’s fluid core. We use a Galerkin method to integrate the Three Potential Description (3PD) for a neutrally, stratified and rotating fluid core of a modified Preliminary Reference Earth Model (PREM). Moreover, the same mathematical tool is used for the computation of the frequencies and displacement amplitudes of the Slichter modes. In the Galerkin formulation of the 3PD, using the divergence theorem, we make use of the natural character of the boundary conditions to reduce the order of derivatives from second to first. To compute the frequencies of the Slichter modes, we solve simultaneously the equations of the inner core motion and the dynamics of the fluid core as described above. The results are compared to those in previous studies and it is shown that in the case of the inertial modes they agree well, which proves the validity of the approach. For the Slichter modes, however, it is shown that the results are significantly different from previous work for a similar Earth model. We have also plotted the displacement eigenfunctions for the motion of the fluid in the fluid core during the Slichter oscillations. It is shown that the pattern of motion is consistent with the motion of the inner core, which serves as a second test of the validity of our results. / x, 105 leaves : ill. ; 29 cm

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Thesis (Ph. D.)--University of Washington, 1991. / Vita. Includes bibliographical references (leaves [94]-98).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Mark E. Mear. Vita. Includes bibliographical references. Also available from UMI.

Thesis (Ph.D.)--University of Wyoming, 2009. / Title from PDF title page (viewed on June 17, 2010). Includes bibliographical references (p. 89-96).

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 128-134).

Thesis (M.S.)--Rochester Institute of Technology, 2006. / Typescript. Includes bibliographical references (leaves 132-137).

Thesis (M.Sc.)--York University, 2005. Graduate Programme in Industrial & Applied Mathematics. / Typescript. Includes bibliographical references (leaves 88-92). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url%5Fver=Z39.88-2004&res%5Fdat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11806

Thesis (MSc (Mathematics))--University of Stellenbosch, 2007. / In this thesis, we study the numerical approximation of indefinite integrals with algebraic or logarithmic end-point singularities. We show the derivation of the two quadrature formulas proposed by Haber based on the sinc method, as well as, on the basis of error analysis, by means of variable transformations (Single and Double Exponential), the derivation of two other formulas: Stenger’s Single Exponential (SE) formula and Tanaka et al.’s Double Exponential (DE) sinc method. Important tools for our work are residue calculus, functional analysis and Fourier analysis from which we state some standard results, and give the proof of some of them. Next, we introduce the Paley-Wiener class of functions, define the sinc function, cardinal function, when a function decays single and double exponentially, and prove some of their interesting properties. Since the four formulas involve a conformal transformation, we show how to transform from the interval (−¥,¥) to (−1, 1). In addition, we show how to implement the four formulas on two computational examples which are our test problems, and illustrate our numerical results by means of tables and figures. Furthermore, from an application of the four quadrature formulas on two test problems, a plot of the maximum absolute error against the number of function evaluations, reveals a faster convergence to the exact solution by Tanaka et al.’s DE sinc method than by the other three formulas. Next, we convert the indefinite integrals (our test problems) into ordinary differential equations (ODE) with suitable initial values, in the hope that ODE solvers such as Matlabr ode45 or Mathematicar NDSolve will be able to solve the resulting IVPs. But they all failed because of singularities in the initial value. In summary, of the four quadrature formulas, Tanaka et al.’s DE sinc method gives more accurate results than the others and it will be noted that all the formulas are applicable to both singular and non-singular integrals.