of Online Publication: 31/03/2008 Keywords: NAG, Maple, MATLAB Authors: Mike Dewar Pages: 17-26 The NAG Library is a collection of 1533 numerical subroutines, comprising almost a million lines of code which has undergone continued evolution, and been exercised by a large user community for over 36 years. It represents a vast knowledge base, whose re-invention […]
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
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
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.
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
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,
Date of Online Publication: 31/03/2006 Keywords: Ordinary differential equations, boundary value problems, collocation, residual, Authors: J. Kierzenka, L.F. Shampine Pages: 27-41 We describe the algorithms and implementation of the bvp5c program for solving boundary value problems (BVPs) for ordinary differential equations. A remarkable relationship between scaled residual and true error is established for the four-point
Date of Online Publication: 31/03/2008 Keywords: Ordinary differential equations; initial value problems; numerical differential, equations; numerical integration; extrapolation methods; rounding error accumulation; NDSolve Authors: Mark Sofroniou, Giulia Spaletta Pages: 105-121 This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up
Date of Online Publication: 31/03/2008 Keywords: MOL, Method of Lines Authors: R. Knapp Pages: 43-59 Mathematica’s NDSolve command includes a general solver for partial differential equations based on the method of lines. Starting from a symbolic expression for the PDE a symbolic general representation of the spatial discretization is constructed which is finalized once the
Date of Online Publication: 31/03/2008 Keywords: Initial-value problem, ordinary differential equation, event location, root-finding, generalized eigenvalues, companion matrix pencil, Hermite interpolation problem,B�zout matrix Authors: Robert M. Corless, Azar Shakoori, D.A. Aruliah, Laureano Gonzalez-Vega Pages: 1-16 Continuous extensions are now routinely provided by many IVP solvers, for graphical output, error control, or event location. Recent developments