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...
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...
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...