A type insensitive code for delay differential equations basing on adaptive and explicit Runge-Kutta interpolation methods
type: Item
instance of: scholarly article
title: A type insensitive code for delay differential equations basing on adaptive and explicit Runge-Kutta interpolation methods
zbMATH Open document ID: 0662.65072
DOI: 10.1007/BF02251253
author: R. Weiner
author: K. Strehmel
published in: Computing
publication date: 1988-01-01T00:00:00Z
review text: An algorithm based on a third order linearly implicit Runge-Kutta method with Lagrange or Hermite interpolation of degrees 2 or 3, respectively for the retarded argument for stiff delay equations and an explicit Runge-Kutta interpolation method for nonstiff delay equations is proposed. An automatic stiffness detection and stepsize control based on Richardson extrapolation is presented and some numerical results and comparisons with other codes are given.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 4082877
zbMATH Keywords: third order linearly implicit Runge-Kutta method
zbMATH Keywords: stiff delay equations
zbMATH Keywords: explicit Runge-Kutta interpolation method
zbMATH Keywords: nonstiff delay equations
zbMATH Keywords: automatic stiffness detection
zbMATH Keywords: stepsize control
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: numerical results
zbMATH Keywords: comparisons with other codes
reviewed by: Kevin Burrage
describes a project that uses: ODEPACK
MaRDI profile type: Publication
cites work: Numerical solution of retarded initial value problems: Local and global error and stepsize control
cites work: Special stability problems for functional differential equations
cites work: P-stable and P[\(\alpha\),\(\beta]\)-stable integration/interpolation methods in the solution of retarded differential-difference equations
cites work: Q3740148
cites work: Numerical treatment of delay differential equations by Hermite interpolation
cites work: Partitioned Runge-Kutta methods with stiffness detection and stepsize control
cites work: Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
cites work: The Stability of Difference Formulas for Delay Differential Equations
cites work: Q3355163
cites work: Q3703223
full work available at URL: https://doi.org/10.1007/bf02251253
OpenAlex ID: W1547152071
description: scientific article; zbMATH DE number 4082877