This paper deals with the mathematical analysis of mathematical models in continuum physics which are described by partial differential equations, in one space dimension, with additional random noise. The first part of the paper provides the framework for the mathematical modelling of a large...

An Expert System can be defined “bottom up” as a software package that uses a knowledge base and inference engine, or “top down” as one that attempts to simulate the reasoning of a human expert. PLOD, a package for solving systems of ordinary differential equations satisfies the second...

In this paper a model for simulation of electromagnetic systems is proposed. The magnetic equations solved with the help of the finite element method are coupled with the electric equations of the external circuit. The Newton Raphson algorithm is used to take into account the nonlinearities of...

Many important physical problems exhibit phenomena that require local grid resolution. Activity indicators are used by local grid refinement schemes to determine where to place or remove local grids, in order to achieve a better accuracy on the numerical procedure. We present a methodology for...

A method is presented for using a single (0, 1) uniform random number to yield stochastically independent random numbers having a given finite distribution. The adaptation of the alias method to the given procedure is outlined. An application to simulate Brownian motion is given.

By stochastic perturbations of white noise type, a nonlinear system will with probability 1 leave any bounded domain of state space that contains a stable equilibrium of the system. The escape time and its statistics are a measure for the stochastic stability of the system. Its statistical...

There are many reasons why experts examine data. This report describes an expert system that was designed as an assistant to an expert, to help with the problem of too much data and too little time, by automating many of the processing procedures and managing the information and data that is...

The aim of the paper is to determine the solution of the Sylvester matric algebraic equation via the Kronecker algebra. The main result points out that, if the unknown matrix is (p × q), the solution can be determined through the inversion of a (min(p, q) × min(p, q)) matrix.

A discrete-time finite element collocation method is applied to the equations of one-dimensional nonlinear thermoviscoelasticity. The existence and uniqueness of the approximate solution are proved and error estimates are established for approximation in a function space consisting of C1...

We are developing an expert system environment for solving elliptic partial differential equations (PDEs) defined on two and three dimensional domains on MIMD type parallel machines. According to its design objectives, it will provide a uniform programming environment for implementing parallel...