Volume 03

Approximation Capabilities of Neural Networks

Issues 3-4 Volume 03

Abstract: Algorithm-based computers are programmed, i.e., there must be a set of rules which, a priori, characterize the calculation that is implemented by the computer. Neural computation, based on neural networks, solve problems by learning, they absorb experience, and modify their internal structure in order to accomplish a given task. In the learning process, the […]

Numerical Aspects of the Coeffcient Computation for LMMs

Issues 3-4 Volume 03

Keywords: Linear Multistep Methods, Boundary Value Methods, Conditioning, Vandermonde matrix, Bernstein polynomials, Bjork-Pereyra algorithm Abstract: The numerical solution of Boundary Value Problems usually requires the use of an adaptive mesh selection strategy. For this reason, when a Linear Multistep Method is considered, a dynamic computation of its coeffcients is necessary. This leads to solve linear

PREFACE_2

Issues 1-2 Volume 03

Date of Online Publication: 31/03/2008 Keywords: Numerical Computing, Problem Solving Environments, Differential Equations Authors: L.F. Shampine Pages: i This special volume is devoted to computation in problem solving environments (PSEs) with emphasis on differential equations. Exploiting the amazing developments in computer hardware and graphical interfaces, PSEs try to make it as easy as possible to

The SCHOL Project at the University of Maryland: Using Mathematical Softwar

Issues 1-2 Volume 03

Date of Online Publication: 31/03/2008 Keywords: Differential equations course, computer supplement, mathematical software Authors: Ronald L. Lipsman, John E. Osborn, and Jonathan M. Rosenberg2 Pages: 81-103 At the University of Maryland, we have experimented over the last 16 years with the use of several problem-solving environments (PSEs) to enhance the teaching and enrich the syllabus

Some Computational Aspects of Helly-type Theorems

Issues 3-4 Volume 03

Keywords: Helly’s theorem; set of width; set of constant width Mathematics Subject Classifcation: 52A01 Abstract: In this paper, we prove that, for a given positive number d, if every n + 1 of a collection of compact convex sets in IEn contain a set of width d (a set of constant width d, respectively) simultaneously,

pythNon: A PSE for the Numerical Solution of Nonlinear Algebraic Equations

Issues 1-2 Volume 03

Date of Online Publication: 31/03/2008 Keywords: Nonlinear algebraic equations, Newton’s method, problem-solving environment Authors: Raymond J. Spiteri and Thian-Peng Ter Pages: 123-137 Nonlinear algebraic equations (NAEs) occur routinely in many scientific and engineering problems. The process of solving these NAEs involves many challenges, from finding a suitable initial guess to choosing an appropriate convergence criterion.

Automatic Code Generation and Optimization in Maple

Issues 1-2 Volume 03

Date of Online Publication: 31/03/2008 Keywords: Maple, C, Code Conversion, Code Optimization Authors: Allan Wittkopf Pages: 167-180 In this article we discuss the advantages (and pitfalls) in developing code optimization and Maple to C conversion programs for Maple procedures, specifically those required for numerical differential equation solution. Special treatment related to code optimization for large

Solving Differential Algebraic Equations by Taylor

Issues 1-2 Volume 03

Date of Online Publication: 31/03/2008 Keywords: Differential algebraic equations (DAEs), structural analysis, Taylor series, automatic differentiation Authors: Nedialko S. Nedialkov, Nedialko S. Nedialkov Pages: 61-80 The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit,

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