Output in extrapolation codes
type: Item
instance of: scholarly article
title: Output in extrapolation codes
zbMATH Open document ID: 0533.65049
DOI: 10.1016/0898-1221(83)90128-1
publication date: 1983-01-01T00:00:00Z
review text: Whereas some codes for the numerical integration of the initial value problem, such as the Adams code, are largely influenced by the places at which the user requires an answer because of the feasibility of applying an interpolating polynomial, the same is not true of certain others, such as Runge-Kutta methods. After describing how fixed-output Runge-Kutta codes can be affected by output requirements, the authors show how the work of P. Deuflhard on variable order codes based on extrapolation of the midpoint rule enables a reduction in the sensitivity to output. They also complement Deuflhard's variation of order by deriving ''interpolating'' Runge-Kutta formulae. Numerical results show that the resulting code is much less sensitive to output than existing codes, particularly at cruder tolerances and with relatively dense output.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 3846775
zbMATH Keywords: numerical results
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: variable order codes
zbMATH Keywords: extrapolation of the midpoint rule
author: L. F. Shampine
author: Lorraine S. Baca
author: Hans-Jörg Bauer
MaRDI profile type: Publication
full work available at URL: 0898-1221(83)90128-1
OpenAlex ID: W2077245175
cites work: Numerical treatment of ordinary differential equations by extrapolation methods
cites work: OnA-stable implicit Runge-Kutta methods
cites work: Order and stepsize control in extrapolation methods
cites work: Comparing Numerical Methods for Ordinary Differential Equations
cites work: Q4117285
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 3846775