No description available.

Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This paper is divided into five sections. It is concerned with the derivation and application of a formula known as Quadrature by Differentiation. Section One derives the basic formula by applying integration by parts to a suitably chosen 2n^th. degree polynomial. By applying this method to a polynomial of degree m + n, Hummel and Seebeck's Generalized Taylor Expansion is obtained and shown identical with the Quadrature Formula when m is set equal to n. Finally the quadrature approximation is proved convergent if f(x) is analytic in a certain domain of the complex plane. Section Two deals with the representation of certain elementary functions using quadrature methods. These expansions, because they have integer coefficients and appear in a rational form, are far easier to compute than the corresponding Maclaurin Series with the same degree of accuracy. Section Three uses quadrature methods to solve ordinary differential equations whose boundary data are given at a single point. The method that is devoloped is a variation of the predictor corrector type. It is very accurate and is easily extended to solve almost every type of initial value problem. Section Four treats the linear "Two Point" and eigenvalue problem. This is accomplished by transforming the given differential equation into a system of linear algebraic relationships between the known and unknown boundary conditions. This section also deals briefly with the non linear "Two Point Problem" suggesting a iterative method, based on the results of Section Three, to obtain the missing boundary data. Section Five improves on something that Quadrature by Differentiation already is; an accurate integration formula. This is achieved by replacing derivatives with central differences. The final result is three integration formulas based only on the tabular values of the function being integrated. Since these formulas are derived using the basic interval, xg< x < xg + h, integration can be extended into s successive intervals using the same or different values of h. / 2031-01-01

As technological advances throughout the field of satellite geodesy improve the accuracy of satellite measurements, numerical methods and algorithms must be able to keep pace. This becomes increasingly important for high precision applications, such as high degree/order gravity field recovery. Currently, the Gravity Recovery and Climate Experiment's (GRACE) dual one-way microwave ranging system can determine changes in inter-satellite range to a precision of a few microns; however, with the advent of laser measurement systems nanometer precision ranging is a realistic possibility. With this increase in measurement accuracy, a reevaluation of the accuracy inherent in the numerical integration algorithms is necessary. This study attempts to quantify and minimize these numerical errors in an effort to improve the accuracy of modeling and propagation of various orbital perturbations; helping to provide further insight into the behavior and evolution of the Earth's gravity field from the more capable gravity missions in the future. The numerical integration errors are examined for a variety of satellite accelerations. The propagation of orbits similar to those of the GRACE satellites using a gravitational model that assumes the Earth is a perfect sphere show integration errors, using double precision numerical representations, on the order of 1 micron in inter-satellite range and 0.1 nanometers per second in inter-satellite range-rate. In addition, when the Earth's gravitational field is formulated in spherical harmonics these numerical integration errors begin to contaminate signals to due harmonics approximately above degree 220, for an orbit at GRACE altitudes. Also, when examining the effect of mass anomalies on the Earth's surface, simulated as point masses, it is apparent that numerical integration methods are easily capable of resolving point mass anomalies as small as 0.05 gigatonnes. Finally, a numerical integration procedure is determined to accurately simulate the effect of numerous, small step accelerations applied to the satellite's center of mass due to misalignment and misfiring of the attitude thrusters. Future studies can then use this procedure as a metric to evaluate the accuracy and effectiveness of an accelerometer in reproducing these non-gravitational forces and how these errors might affect gravity field recovery. / text

Thesis (Ph. D.)--University of Wisconsin, 1964. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (p. 78-81).

[by] Manuel V. Cerillo. / On t.p. "n?" is subscript. On t.p. expression "W(s,[tau]1,[tau]2,...,[tau]n?)" is superscript.

Thesis (Ph.D.)--University of Waikato, 2008. / Title from PDF cover (viewed May 24, 2008) Includes bibliographical references (p. [150]-154)

Thesis (M.S.)--Georgia Southern University, 2008. / "A thesis submitted to the Graduate Faculty of Georgia Southern University in partial fulfillment of the requirements for the degree Master of Science." Directed by Steven Damelin. ETD. Includes bibliographical references (p. 41-42)

Thesis (M.Sc.)--Memorial University of Newfoundland, 2002. / Restricted until May 2003. Bibliography: leaves 88-91.

Thesis (M.S. in Engineering Acoustics and M.S. in Electrical Engineering)--Naval Postgraduate School, June 1990. / Thesis Advisor(s): Miller, James H. ; Chiu, Ching-Sang ; Yang, Chyan. "June 1990." Description based on title screen as viewed on October 20, 2009. DTIC Identifier(s): Acoustic Tomography, Theses, Range Kutta Fehlberg Method, C Programming Language, Macintosh 2 Computers, Transputers, Parallel Processors, Numerical Integration. Author(s) subject terms: Acoustic Tomography, Ray Tracing, Parallel Processing, Gaussian Beams, Transputers. Includes bibliographical references (p. 122-124). Also available online.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. Includes bibliographical references.