This thesis presents an axiomatic approach to the theory of inner measures. In Chapter I, we recognize that an axiomatic approach analogous to that for the theory of outer measures is not appropriate: such an approach ...

The finite element solution of certain two-point boundary value problems is discussed. In order to obtain more accuracy than the linear finite element method can give, an order-h[superscript 4] global superconvergence ...

This thesis is an attempt to establish an abstract model for Lebesgue measure and Baire category. In the introduction, we list several similarities between Lebesgue measurable sets and sets having the property of ...

This thesis contains a study of higher dimensional numerical quadrature, especially two dimensional Gregory quadrature. In Chapter I, we discuss the problem of approximation and integration, the reasons why numerical ...

The principal question discussed in this dissertation is the problem of characterizing the existence of admissible Frechet differentiable norms on Banach spaces. In the first chapter the basic concepts of normed linear ...

This thesis deals primarily with solving systems of autonomous ordinary nonlinear differential equations arising in Celestial Mechanics initial value problems using various finite-difference techniques. Those methods ...

Higher order finite difference methods are discussed with respect to speed and accuracy when used in the solution of elliptic partial differential equations. Although fast direct methods for solving elliptic ...