Maple 8 and Maplets: A New Use of Computer Algebra for Teaching Mathematics and Science (2009)
To begin this exploration of Maplets, you should be aware that some of the new features in Maple 8 are implemented as Maplets. The new interactive command in the plots package provides a more...
Douglas B. Meade, Hill Substitution Cypher
& MATH ATH � � Computer science/engineering students … � � see relevant and interesting applications of mathematics � � learn some new mathematics � � motivated to take more...
Maple Tools for Use in Conjecture Testing and Iteration Mappings in Number Theory (2009)
Douglas B. Meade, Charles A. Nicol
The purpose of this paper is to i) introduce procedures which can be used in the investigation of a general class of problems in number theory and ii) illustrate some of the powerful new features of...
Numerical, Graphical and Symbolic Analysis of Bernoulli Equations 1 (2008)
The problem discussed in this paper is an extension of a homework problem in a sophomorelevel course in di erential equations. The exercises at the end of the section on the improved Euler's...
A COMPARISON OF RADIATION BOUNDARY CONDITION STRATEGIES FOR HELMHOLTZ EQUATIONS (2008)
Catherine Piellusch-castle, Yin-shang Liu, Bernd Lichtenberg, Douglas B. Meade, Kevin J. Webb
1. Introduction. Many problems in electromagnetics involve the solution of a wave equation in an exterior domain. The unbounded computational domain complicates the search for e cient numerical...
Differential Equations in the New Millennium: the Parachute Problem* (2008)
Douglas B. Meade, Allan A. Struthers
Introductory courses in differential equations have traditionally consisted of a long list of solution techniques for special equations. This characterization is becoming increasingly inaccurate as...
Differential Equations in the New Millennium: The Parachute Problem (2007)
Douglas B. Meade, Allan A. Struthers
. Introductory courses in differential equations have traditionally consisted of a long list of solution techniques for special equations. This characterization is becoming increasingly inaccurate as...
An S-I-R Model for Epidemics with Diffusion to Avoid Infection and Overcrowding (2007)
Douglas B. Meade, Fabio A. Milner
A model for an epidemic of S--I--R type is described in which susceptibles move to avoid the infection and all individuals move away from overcrowded regions. Some qualitative properties of the...
this paper is to demonstrate how a traditional problem from a traditional text can be modified to provide a more realistic view of the applicability of differential equations. Almost any...
Numerical, Graphical and Symbolic Analysis of Bernoulli Equations (2007)
this paper is an extension of a homework problem in a sophomorelevel course in differential equations. The exercises at the end of the section on the improved Euler's method for solving...
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The first author was supported by grants from the National Security Agency.
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The rst author was supported by grants from the National Security Agency. 1
Irreducibility Testing of Lacunary 0,1-Polynomials (2007)
Michael Filaseta, Douglas B. Meade
1 The first author was supported by grants from the National Security Agency.
Maple Tools for Use in Conjecture Testing and Iteration Mappings in Number Theory (2007)
Douglas B. Meade, Charles A. Nicol
this paper is to i) introduce procedures which can be used in the investigation of a general class of problems in number theory and ii) illustrate some of the powerful new features of Maple V,...
Second-Order Transmission Conditions for the Helmholtz Equation (1998)
. We present an iterative nonoverlapping domain decomposition method with second-order Robin-type transmission conditions for the scalar Helmholtz equation in two dimensions. The analysis of the...
Second-Order Transmission Conditions for the Helmholtz Equation (1998)
We present an iterative nonoverlapping domain decomposition method with second-order Robin-type transmission conditions for the scalar Helmholtz equation in two dimensions. The analysis of the...
Second-order transmission conditions for the Helmholtz equation (1997)
Several domain decomposition methods for the solution of elliptic problems have been proposed, analyzed, and successfully implemented during the past decade [BW86, BPS86, GW88, HTJ88, Lio88, Lio90]....
Second-order transmission conditions for the Helmholtz equation (1997)
Abstract. We present an iterative nonoverlapping domain decomposition method with second-order Robin-type transmission conditions for the scalar Helmholtz equation in two dimensions. The analysis of...
Maple and the parachute problem: modelling with an impact (1997)
The \parachute problem " involves a rst-order ODE in which the coe cient of air resistance is a piecewisede ned function. This paper focuses on the use of Maple's symbolic, numeric, and...
Bernd Lichtenberg, Kevin J. Webb, Douglas B. Meade, Andrew F. Peterson
Numerical solutions for open-region electromagnetic problems based on differential equations require some means of truncating the computational do-main. A number of local Radiation Boundary...
The Shooting Technique for the Solution of Two-Point Boundary Value Problems (1996)
Douglas B. Meade, Bala S. Haran, Ralph E. White
this paper is to describe the shooting method and its Maple implementation, shoot.
Bernd Lichtenberg, Kevin J. Webb, Douglas B. Meade, Andrew F. Peterson
Numerical solutions for open-region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions...
The shooting technique for the solution of two-point boundary value problems (1996)
One of the strengths of Maple is its ability to provide a wide variety of information about di erential equations. Explicit, implicit, parametric, series, Laplace transform, numerical, and graphical...
Douglas B. Meade, G. William Slade, Andrew F. Peterson, Kevin J. Webb
The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss--Turkel condition are evaluated. These boundary conditions permit the approximate solution of...
Douglas B. Meade, Andrew F. Peterson, Catherine Piellusch-Castle
Wave equations in exterior domains typically include a boundary condition at infinity to ensure the well-posedness of the problem. An obstacle to the efficient computation of solutions is the...
Douglas B. Meade, G. William Slade, Andrew F. Peterson, Kevin J. Webb
Abstract | The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss{Turkel condition are evaluated. These boundary conditions per-mit the approximate...
Numerical Implementation of a Conformable Two-Dimensional Radiation Boundary Condition (1995)
Bernd Lichtenberg, Kevin J. Webb, Andrew F. Peterson, Douglas B. Meade
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...
A Comparison of Radiation Boundary Condition Strategies for Helmholtz Equations (1994)
Catherine Piellusch-castle, Yin-shang Liu, Bernd Lichtenberg, Douglas B. Meade, Kevin J. Webb
this paper we consider a number of radiation boundary conditions (RBCs). In particular, we present a procedure that can be used to extend any boundary condition for a circular boundary to a general...