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...
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...
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
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...
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...
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.
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...
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
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