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Filtering by: Subject Wave equations -- Numerical solutions Remove constraint Subject: Wave equations -- Numerical solutions Degree Name Doctor of Philosophy (Ph.D.) Remove constraint Degree Name: Doctor of Philosophy (Ph.D.)

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  • 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

  • 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:
    initial data and the lifespan of the classical solution for the nonlinear wave equation. 3 Along with

  • 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

  • Irregular points in wavemaker boundary value problem

    Creator:
    Tanaka, Yoshihiro
    Abstract:
    A global solution is presented that accurately accounts for the singular behavior at all irregular points. The linearized boundary value problem in a semi-infinite strip in the physical plane is transformed into a smooth unit disk by two successive conformal mappings. The global solution results from a Fredholm integral equation...
    Resource Type:
    Dissertation
    Full Text:
    mappings. The global solution results from a Fredholm integral equation that is obtained from Green's

  • Existence of a solution to a variational data assimilation method in two-dimensional hydrodynamics

    Creator:
    Hagelberg, Carl R.
    Abstract:
    The main result of this paper is a proof of the existence of a solution generated by a method for the variational assimilation of observational data into the two-dimensional, incompressible Euler equations. The data are assumed to be given by linear (measurement) functionals acting on the space of functions representing...
    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:
    Mathematics presented on September 3, 2003. - Title: Numerical Inversion of Laplace Transforms By the

  • Time domain simulation of Maxwell's equations by the method of characteristics

    Creator:
    Orhanovic, Neven
    Abstract:
    A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the...
    Resource Type:
    Dissertation
    Full Text:
    solution, full-wave numerical methods can serve a number of other important purposes. They can be used as

  • Skew Brownian motion and branching processes applied to diffusion-advection in heterogenous media and fluid flow

    Creator:
    Ramirez, Jorge M.
    Abstract:
    This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics. In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...
    Resource Type:
    Dissertation
    Full Text:
    accurate numerical calculations of the solution. The second manuscript considers an advection-diffusion