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  • A nonlinear shallow water wave equation and its classical solutions of the cauchy problem

    Creator:
    Crow, John A.
    Abstract:
    A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves over a variable topography. As the usual assumptions of a perfect fluid and an irrotational flow are not made, the resulting model equation is dissipative due to the presence of a viscous boundary layer at...
    Resource Type:
    Dissertation
    Full Text:
    . Guenther A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves

  • Nonlinear internal waves on the continental shelf: observations and KdV solutions

    Creator:
    O'Driscoll, Kieran
    Abstract:
    Numerical solutions of the Korteweg-de Vries (KdV) and extended Korteweg-de Vries (eKdV) equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal...
    Resource Type:
    Masters Thesis

  • Automated rigorous solutions to nonlinear equations

    Creator:
    Cullop, Paul Wayne
    Abstract:
    We will consider the implementation of a computer program to solve a nonlinear algebraic system of N equations and unknowns. The program involves the use of a parameter, Newton's method, and an automatic change of parameter. Also considered are rigorous error bounds for the answer. The program was implemented and...
    Resource Type:
    Masters Thesis
    Full Text:
    ) ./ (Date) Title: AUTOMATED RIGOROUS SOLUTIONS TO NONLINEAR EQUATIONS Redacted for privacy Abstract

  • An analysis of accuracy of finite difference and finite element methods for the wave equation

    Creator:
    Minei, Marvin
    Abstract:
    In this paper, Fourier analysis is used to investigate various approximation methods for the one- and two-dimensional wave equations. The spatial derivatives are approximated by the second order centered finite difference method, the linear and quadratic finite element methods, and the fourth order centered finite difference method. The approximation schemes...
    Resource Type:
    Masters Thesis
    Full Text:
    element methods for the wave equation AN ABSTRACT OF THE THESIS OF Marvin Minei for the degree of

  • Stochastic analysis of a nonlinear ocean structural system

    Creator:
    Lin, Huan
    Abstract:
    Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from a probabilistic perspective. A multi-point-moored ocean structural system under regular and irregular wave excitations is analytically examined via a generalized stochastic Melnikov function and Markov...
    Resource Type:
    Dissertation
    Full Text:
    the nonlinear governing equation with respect to time. A large number of sample response

  • The Davey-Stewartson equations : a numerical study

    Creator:
    White, Peter W.
    Abstract:
    In 1974 Davey and Stewartson used a multi-scale analysis to derive a coupled system of nonlinear partial differential equations which describes the evolution of a three dimensional wave packet in water of a finite depth. This system of equations is the closest integrable two dimensional analog of the well-known one...
    Resource Type:
    Dissertation

  • On an integral equation occuring in the theory of wave propagation

    Creator:
    Weingarten, Fred Wesley
    Resource Type:
    Masters Thesis
    Full Text:
    AN INTEGRAL EQUATION OCCURRING IN THE THEORY OF WAVE PROPAGATION Abstract approved (Major professor

  • A computer subroutine for the numerical solution of nonlinear Fredholm equations

    Creator:
    Tieman, Henry William
    Resource Type:
    Masters Thesis
    Full Text:
    E [a, b] and F nonlinear, is a nonlinear Fredholm equation of the second kind. Very few equations

  • Fractal solutions to the long wave equations

    Creator:
    Ajiwibowo, Harman
    Abstract:
    The fractal dimension of measured ocean wave profiles is found to be in the range of 1.5-1.8. This non-integer dimension indicates the fractal nature of the waves. Standard formulations to analyze waves are based on a differential approach. Since fractals are non-differentiable, this formulation fails for waves with fractal characteristics....
    Resource Type:
    Dissertation
    Full Text:
    the fractal dimension with the nonlinearity of the waves suggests using a nonlinear wave equation. We

  • The nonlinear wavemaker problem

    Creator:
    Owen, Amy M.
    Abstract:
    The two dimensional wavemaker problem on a finite domain is derived for nonlinear waves. A numerical method based on the method of lines is developed and applied to two test problems, the nonlinear surface pressure distribution problem and the nonlinear full-flap wavemaker problem. The solutions yield information about the fluid...
    Resource Type:
    Masters Thesis
    Full Text:
    differential equation (ODE) and the solution of a nonlinear 2x2 system of simultaneous equations. Both have a