Physical Sciences and Mathematics Commons^™

Stable Predictor-Corrector Methods For First Order Ordinary Differential Equations, Terrell Lester Carlson

Masters Theses

"Because of the wide variety of differential equations, there seems to be no numerical method which will affect the solution best for all problems. Predictor-corrector methods have been developed which utilize more ordinates in the predictor and corrector equations in the search for a better method.

These methods are compared for stability and convergence with the well known methods of Milne, Adams, and Hamming"--Abstract, page ii.

A Study Of The Development Of A Heuristic Program That Solves Symbolic Laplace Transformation Problems, Arthur E. Zackrison

Masters Theses

"A medium-speed general purpose digital computer (IBM 1620 Model II) was programmed to solve symbolic Laplace transformation problems. Although the applied mathematician and modern engineer has many uses for the symbolic solution of a problem, the potential of symbolic manipulation by a computer has not yet been sufficiently developed to help them because of many problems. This paper discusses the program and based on the author’s experience with it’s [sic] performance, clarifies the position of several of these difficulties and reaches some conclusions concerning computer solution of such problems"--Abstract, page ii.

The Memory Unit Of A Digital Computer, Bobby Ridgell

Honors Theses

Since the development of the first modern digital computer in August 1944, the digital computer has become one of the most essential machines of the modern day. According to Edmund Berkeley and Lawrence Wainwright it is one of the two events by which the twentieth century will be remembered. This development has also led to what has been called the Second Industrial Revolution. That so much importance should be placed on one development is extraordinary, but the far reaching effects of the digital computer are also extraordinary.

A Comparison Of The Lr And Qr Transformations For Finding The Eigenvalues For Real Nonsymmetric Matrices, Susan Clara Hanson

Masters Theses

"The LR and QR algorithms, two of the best available iterative methods for finding the eigenvalues of a nonsymmetric matrix associated with a system of linear homogeneous equations, are studied. These algorithms are discussed as they apply to the determination of the eigenvalues of real nonsymmetric matrices.

A comparison of the speed and accuracy of these transformations is made. A detailed discussion of the criterion for convergence and the numerical difficulties which may occur in the computation of multiple and complex conjugate eigenvalues are included.

The results of this study indicate that the QR algorithm is the more successful method …

A Simulation Study Of A Proposed Computer Installation, John Edward Hawthorne

Masters Theses

"The operation of a data processing center has been studied with the objective of investigating the effect of various facilities, job loads, and operating policies as measured by job turnaround time. The mechanism for study was digital computer simulation.

This thesis purports to review the technology of simulation and the associated computer techniques, defines the problem and the alternatives available, and analyzes the results derived from the experiments.

Conclusions drawn from this study support the current practice of a functioning data processing center"--Abstract, page ii.

Comparative Analysis Of Numerical Integration Techniques, Edward Lee Sartore

Masters Theses

"When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson's rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by √1-x ², or as a function g(x) times (1-x)^α (l+x)^ß , where α and ß are some real numbers >1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and …

Error Analysis Of Rational Approximations Of Functions With Emphasis On Minimax Techniques, Mary Frances Good

Masters Theses

"This study examines the various considerations which are made when a function is approximated by a rational function. None of the four approximations considered here gives both a rapidly calculated approximation and one in which the maximum magnitude of the error function over a given interval is a minimum.

The second algorithm of Remes produces a sequence of rational approximations which converge to the rational approximation that minimizes the maximum magnitude of the error function for a given number of parameters to be calculated if the initial approximation in the sequence is chosen properly. Several rational function approximations are investigated …

Economic Analysis Of Alternative Flood Control Measures By Digital Computer, Thomas M. Rachford

KWRRI Research Reports

The purpose of this project was to develop a digital computer program for selecting the optimum combination of flood proofing, flood-plain land use, channel improvement, and residual flood damage for a given floodplain. Based on economic efficiency, the optimum policy is selected for each planning unit of the total flood-plain for each period of time called a planning stage. The program was written in Fortran IV for the IBM 7040 and the University of Kentucky Computing Center compiler. The program requires about 23,000 words of core storage and about 30 seconds of execution time per planning-unit-stage for typical conditions. The …