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Filtering by: Subject Nonlinear wave equations Remove constraint Subject: Nonlinear wave equations Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics

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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

  • 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

  • The Variable Speed Wave Equation and Perfectly Matched Layers

    Creator:
    Kim, Dojin
    Abstract:
    A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain. We introduce a new formulation from regularizing the classical Un-Split...
    Resource Type:
    Dissertation
    Full Text:
    Doctor of Philosophy in Mathematics presented on June 4, 2015. Title: The Variable Speed Wave Equation

  • 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

  • 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

  • Numerical inversion of laplace transforms by the trapezoidal-type methods

    Creator:
    Lin, FuSen F.
    Abstract:
    In this dissertation, we investigate three numerical methods for inverting the Laplace transform. These methods are all based on the trapezoidal-type approximations to the Bromwich integral. The first method is the direct integration method: It is a straightforward application of the trapezoidal rule to the Bromwich integral, followed by convergence...
    Resource Type:
    Dissertation
    Full Text:
    have s= +(_1)/c_1Lak= +R1. Again, we multiply by 22 on both sides of the equation (1.11) and then

  • 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

  • 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

  • Construction and numerical simulation of a two-dimensional analogue to the KdV equation

    Creator:
    Black, Wendy
    Abstract:
    Arising from an investigation in Hydrodynamics, the Korteweg-de Vries equation demonstrates existence of nonlinear waves that resume their profile after interaction. In this thesis, the classical equations governing wave motion are the starting point for the development of an analogue of the KdV that describes the evolution of a wave...
    Resource Type:
    Dissertation