Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 103-109).

Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 73-75). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 140-146). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 225-235). Also available in print.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

No description available.

Thesis (M.A.)--Boston University / The problem of finding the solution to a general eliptic type partial differential equation, when the boundary values are given, is generally referred to as the Dirichlet Problem. In this paper I consider the special eliptic equation of ∇2 J=0 which is Laplace's equation, and I limit myself to the case of two dimensions. Subject to these limitations I discuss five proofs for the existence of a solution to Laplace's equation for arbitrary regions where the boundary values are given. [TRUNCATED]

In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one--way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one--way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one--way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one--way wave equations are solved with GO with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge-Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is just O(ω1/p) for a p-th order Runge-Kutta method. This has been confirmed by numerical experiments.

No description available.

The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of accuracy of the compact schemes employed.