Polynomial and rational interpolation in the numerical solution of stiff systems
type: Item
instance of: scholarly article
title: Polynomial and rational interpolation in the numerical solution of stiff systems
zbMATH Open document ID: 0678.65050
DOI: 10.1016/0096-3003(89)90122-7
author: S. D. Colquitt
author: Jack Williams
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: In the numerical solution of initial value problems the efficiency of codes can be improved by using interpolants. In this article the authors discuss the accuracy of the polynomial interpolation scheme used in standard variable order, variable stepsize BDF codes for stiff problems, where orders range from one to five. In particular the strategy used in the NAG code is considered and shown to be reliable and robust on a large number of test problems. For the case of monotonic solution components, a comparison is made with a particularly simple interpolation scheme based on a rational quadratic.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4111927
zbMATH Keywords: rational interpolation
zbMATH Keywords: numerical results
zbMATH Keywords: backward differentiation formula method
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: variable order, variable stepsize BDF codes
zbMATH Keywords: stiff problems
zbMATH Keywords: NAG code
zbMATH Keywords: monotonic solution
zbMATH Keywords: comparison
reviewed by: Beate Ruffer-Henn
describes a project that uses: NAG
describes a project that uses: HSL
describes a project that uses: STDTST
describes a project that uses: NSDTST
describes a project that uses: DO2QBF
describes a project that uses: DCO3
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90122-7
OpenAlex ID: W4249402202
cites work: A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
cites work: Two FORTRAN packages for assessing initial value methods
cites work: Interpolants for Runge-Kutta formulas
cites work: Iterative Solution of Linear Equations in ODE Codes
cites work: Practical Aspects of Interpolation in Runge-Kutta Codes
cites work: Piecewise Rational Quadratic Interpolation to Monotonic Data
cites work: An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
cites work: Q3727278
cites work: Q4188664
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description: scientific article; zbMATH DE number 4111927