Index Catalog // ScholarsArchive@OSU

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

MINITRAN : an on-line function translator with capabilities for solving ordinary differential equations

Creator:: Ballance, Jeffrey David
Abstract:: A function translator is presented which was designed for interactive programs which allow functions to be defined on-line. The translator handles functions which are specified by a formula and functions which are specified as the solution to a system of differential equations.
Resource Type:: Masters Thesis
Full Text:: identify the differential equation solution to be used or to specify that the numerical derivative of the

Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations

Creator:: Winter, Lynn Taylor
Abstract:: Interval arithmetic is applied to the problem of obtaining rigorous solutions to integral equations on a computer. The integral equations considered are the linear Fredholm equation of the second kind and the nonlinear Urysohn equation. Techniques are presented which enable the computer to find an approximate solution, prove the existence...
Resource Type:: Masters Thesis
Full Text:: numerical solution of a mathematical problem often involves two aspects. One is a computational scheme

A computer subroutine for the numerical solution of nonlinear Fredholm equations

Creator:: Tieman, Henry William
Resource Type:: Masters Thesis
Full Text:: function x : [a, b] Rn that satisfies this equation. A Computer Subroutine for the Numerical Solution

Computation of the stresses on a rigid body in exterior stokes and oseen flows

Creator:: Schuster, Markus
Abstract:: This paper is about the computation of the stresses on a rigid body from a knowledge of the far field velocities in exterior Stokes and Oseen flows. The surface of the body is assumed to be bounded and smooth, and the body is assumed to move with constant velocity. We...
Resource Type:: Masters Thesis
Full Text:: first equation in (54). By looking at the Stokes equations, one can easily see, that the solution to

Numerical solution of Hodgkin-Huxley's partial differential system for nerve conduction

Creator:: Morton, John Baird
Abstract:: A numerical solution to Hodgkin and Huxley's partial differential system for the propagated action potential is presented. In addition a three dimensional demonstration of the absolute refractory period is given. Lastly, theoretical evidence supporting Rushton's hypothesis is presented.
Resource Type:: Masters Thesis
Full Text:: Numerical Solution of Hodgkin-Huxley's Partial

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

Stability of numerical integration of ordinary differential equations

Creator:: Lathrop, James Frank
Abstract:: The thesis discusses stability of procedures based on linear computing formulas for numerical integration of an ordinary first-order differential equation. The theorems are proved: (1) If the procedure is asymptotically stable it is stable for small positive step size if the Lipschitz number is negative; (2) Relative stability always exists...
Resource Type:: Masters Thesis
Full Text:: the growth of the error. Hamming claims (1, p. 198) that the solution of the differential equation

Solution of unsteady, two-dimensional, inviscid flows

Creator:: Kuo, Ying-Ming
Abstract:: The general theory of characteristics is reviewed for hyperbolic partial differential equations of n independent variables. The application of the theory of characteristics is made to unsteady, two-dimensional, rotational, inviscid flows; unsteady, two-dimensional, irrotational, inviscid flows; and unsteady, axial symmetric, inviscid flows. The characteristic surfaces and the compatibility relations are...
Resource Type:: Masters Thesis
Full Text:: fluid field for numerical solution. There exist char- acteristic surfaces in t, x, y- space. They are

ScholarsArchive@OSU

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

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

MINITRAN : an on-line function translator with capabilities for solving ordinary differential equations

Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations

A computer subroutine for the numerical solution of nonlinear Fredholm equations

Computation of the stresses on a rigid body in exterior stokes and oseen flows

Numerical solution of Hodgkin-Huxley's partial differential system for nerve conduction

The Davey-Stewartson equations : a numerical study

Stability of numerical integration of ordinary differential equations

Solution of unsteady, two-dimensional, inviscid flows

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