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Differential Equations in Airplane Mechanics

Description: In the following report, we will first draw some conclusions of purely theoretical interest, from the general equations of motion. At the end, we will consider the motion of an airplane, with the engine dead and with the assumption that the angle of attack remains constant. Thus we arrive at a simple result, which can be rendered practically utilizable for determining the trajectory of an airplane descending at a constant steering angle.
Date: March 1922
Creator: Carleman, M. T.
Partner: UNT Libraries Government Documents Department

Similar Solutions for the Compressible Laminar Boundary Layer with Heat Transfer and Pressure Gradient

Description: Note applying Stewartson's transformation to the laminar compressible boundary-layer equations and the requirement of similarity, resulting in a set of ordinary nonlinear differential equations previously quoted by Stewartson, but unsolved. The requirements of the system are specified. It is then transformed to an integral system with the velocity ratio as the independent variable.
Date: February 1955
Creator: Cohen, Clarence B. & Reshotko, Eli
Partner: UNT Libraries Government Documents Department

An Elementary Review of the Mathieu-Hill Equation of Real Variable Based on Numerical Solutions

Description: Abstract: description is given of a large number of trajectories of Mathieu's equation made on the ENIAC in 1948 and available at BRL. A large chart describing the behaviour of the solutions is given. The occasion is taken to review the essentials of the Mathieu theory for the benefit of the occasional user-proceeding from the point of view of an inspection of the numerical data.
Date: April 1955
Creator: Zaroodny, Serge J.
Partner: UNT Libraries Government Documents Department

On the Instability of Methods for the Integration of Ordinary Differential Equations

Description: Memorandum presenting an investigation of the instability of methods for the integration of ordinary differential equations. Examples and a criterion for stability of integration methods is provided. The criterion is applied to well-known integration formulas.
Date: April 1956
Creator: Rutishauser, Heinz
Partner: UNT Libraries Government Documents Department

Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance

Description: The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.
Date: 1956
Creator: Haynes, Joe Preston
Partner: UNT Libraries

On the Existence and Uniqueness of Solutions of Two Differential Equations

Description: The purpose of this paper is to study two differential equations. A method of approximation by iteration is used to define sequences of functions which converge to solutions of these equations. Some properties of the solutions are proved for general boundary conditions and certain special solutions are studied in detail.
Date: August 1965
Creator: Keath, Mary Katherine
Partner: UNT Libraries

A Transformation Theory of the Partial Differential Equations of Gas Dynamics

Description: Note presenting a transformation theory of systems of partial differential equations which allows the construction of classes of pressure-density relations depending on parameters for which the equations governing the flow can be transformed into an essentially simpler form, into the system corresponding to the wave equation in the subsonic region, and finally into the form corresponding to the Tricomi equation in the transonic region.
Date: April 1950
Creator: Loewner, Charles
Partner: UNT Libraries Government Documents Department

Mathematical and numerical studies of nonstandard difference equation models of differential equations. Final technical report

Description: This report summarizes the complete research findings of the PI. Included are titles and places of publication of all journal, book, and conference papers, and abstracts. A listing of major conferences and meetings where these research results were reported is also provided.
Date: October 3, 2001
Creator: Mickens, Ronald E.
Partner: UNT Libraries Government Documents Department

The Slowing-Down Distribution of Energetic Nuclei in a Fully Ionized Gas

Description: The steady-state energy distribution is obtained for a group of initially monoenergetic charged particles slowing down in a filly ionized gas. The distribution function is obtained analytically by solving the FokkerPlanck equation in energy space. With reference to thermonuclear reactions, the results obtained suggest that in some situations the contribution of the slowingdown distribution to the reaction rate may be significant. (auth)
Date: May 1, 1958
Creator: Kidder, R. E.
Partner: UNT Libraries Government Documents Department

The Runge-Kutta Method

Description: This paper investigates the Runge-Kutta method of numerically integrating ordinary differential equations. An existence theorem is given insuring a solution to the differential equation, then the theorem is modified to yield an analytic solution. The derivation of the method itself is followed by an analysis of the inherent error.
Date: June 1961
Creator: Powell, Don Ross
Partner: UNT Libraries

Examination of the SCEPTRE and CSMP Programs for Solving the Point-Kinetics Equations with Feedback

Description: Two modeling programs, SCEPTRE and CSMP, are used to solve the point-kinetics equations - - seven coupled nonlinear differential equations - - with a linear-feedback function. The constants used are appropriate for EBR-II; therefore the computational accuracy may be tested against the experimental rod drops. Run-time, versatility, programming ease, and accuracy are criteria used to evaluate the two programs. SCEPTRE is found to be more efficient in run time and CSMP more versatile. The ease of programming is about the same for both programs. The accuracy is nearly equivalent if the optimum integration routines are used.
Date: September 1976
Creator: Walkowski, P. D. & Peterson, B. R. (Bruce R.)
Partner: UNT Libraries Government Documents Department

Comparative Test Results for Two ODE Solvers: EPISODE and GEAR

Description: This is a sequel to the paper ''A comparison of two ODE codes: GEAR and EPISODE,'' and is concerned with the testing of two superficially similar ODE packages, GEAR and EPISODE. Fourteen basic test problems, some with several cases, are the basis for the testing. These problems represent several types-nonlinear systems with real and complex eigenvalues, linear systems with varied diagonal dominance, linear scalar problems, stiff and non-stiff problems, chemical kinetics with and without diurnal effect, and systems arising from the use of the numerical method of lines. Some problems are included in order to examine the options and error returns. The test results are presented in two forms: raw output and a comparative display of operation counts and of timings for the best method in the GEAR package and the best method in the EPISODE package. This approach allows a comparison of the consequences of the fixed-step interpolate strategy (GEAR) for changing step size against the truly variable step size strategy (EPISODE). It is concluded that EPISODE is generally faster than GEAR for problems involving wave fronts or transients on the interior of the interval of integration. For linear or simply decaying problems, these roles are usually reversed.
Date: March 1977
Creator: Byrne, G. D.; Hindmarsh, A. C.; Jackson, Kenneth R. & Brown, H. Gordon
Partner: UNT Libraries Government Documents Department

Existence and multiplicity of solutions for semilinear elliptic boundary value problems

Description: This thesis studies the existence, multiplicity, bifurcation and the stability of the solutions to semilinear elliptic boundary value problems. These problems are motivated both by the mathematical structure and the numerous applications in fluid mechanics chemical reactions, nuclear reactors, Riemannian geometry and elasticity theory. This study considers the problem for different classes of nonlinearities and obtain the existence and multiplicity of positive solutions.
Date: August 1992
Creator: Gadam, Sudhasree
Partner: UNT Libraries

Steepest descent for partial differential equations of mixed type

Description: The method of steepest descent is used to solve partial differential equations of mixed type. In the main hypothesis for this paper, H, L, and S are Hilbert spaces, T: H -> L and B: H -> S are functions with locally Lipshitz Fréchet derivatives where T represents a differential equation and B represents a boundary condition. Define ∅(u)=1/2IIT(u)II^2. Steepest descent is applied to the functional ∅. A new smoothing technique is developed and applied to Tricomi type equations (which are of mixed type).
Date: August 1992
Creator: Kim, Keehwan
Partner: UNT Libraries

Performance and scaling of locally-structured grid methods forpartial differential equations

Description: In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach.
Date: July 19, 2007
Creator: Colella, Phillip; Bell, John; Keen, Noel; Ligocki, Terry; Lijewski, Michael & Van Straalen, Brian
Partner: UNT Libraries Government Documents Department

AN IBM-7090 SUBROUTINE PACKAGE FOR LAGRANGIAN INTERPOLATION

Description: A FORTRAN subroutine was writteni for the purpose of generating a table of data by Lagrangian interpolation in a smaller table of data. There are three options for the interpolation scheme: linear, semilog, and log-log. The number of points to be used in the Lagrangian interpolation is optional. This subroutine provides information for a table lookup, which is usually much less costly than direct computation. (auth)
Date: May 16, 1963
Creator: Penny, S.K. & Emmett, M.B.
Partner: UNT Libraries Government Documents Department

Variable Metric Method for Minimization

Description: A method for determining numerically local minima of differentiable functions of several variables is presented. In the process of locating each minimum, a matrix which characterizes the behavior of the iunction about the minimum is determined. For a region in which the function depends quadratically on the variables, no more than N iterations are required, where N is the number of variables. By suitable choice of starting values and without modification of the procedure, linear constraints can be imposed upon the variables. (auth)
Date: November 1, 1959
Creator: Davidon, W. C.
Partner: UNT Libraries Government Documents Department