In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The complex dynamical behaviors of the system are further investigated by means of eigenvalue structures and various attractors. The chaotic system examined in MATLAB 2010. The Oscillator...

In open region di erential equation problems it is common to limit the computational domain by introducing an arti cial boundary. The arti cal boundary condition must be chosen to produce as little re ection as possible. Numerous ideas have been employed in the search of accurate and e cient radiation boundary conditions (RBCs). A nite element method (FEM) formulation that encompasses many di e...

This report recommends a method of implementing a numerical ground image system which will augment and interface with the Roadway Design System (RDS) developed in a previous research effort by the Texas Highway Department in cooperation with the Federal Highway Administration. Proprietary software packages, a previously developed research system and the scan profile system developed by the Depa...

In the paper we report on a second stage of our efforts towards a library design for the solution of very large set of linear equations arising from the finite difference approximation of elliptic partial differential equations (PDE). Particularly a family of Krylov subspace iterative based methods (in the paper exemplified by the archetypical Krylov space method Conjugate Gradient method) are ...

We put forth a few ideas on coordinate conditions and their implementation in numerical relativity. Coordinate conditions are important for the long time scale simulations of relativistic systems, e.g., for the determination of gravitational waveforms from astrophysical events to be measured by LIGO/VIRGO. We demonstrate the importance of, and propose methods for, the active enforcement of coor...

A novel approach is presented to implement continuous Hop eld neural networks, which are modelled by a system of ordinary di erential equations (ODEs). The simulation of a continuous network in a digital computer implies the discretization of the ODE, which is usually carried out by simply substituting the derivative by the di erence, without any further theoretical justi cation. Instead, the n...