Issues in the numerical solution of evolutionary delay differential equations
type: Item
instance of: scholarly article
title: Issues in the numerical solution of evolutionary delay differential equations
zbMATH Open document ID: 0832.65064
DOI: 10.1007/BF02988625
author: Christopher T. H. Baker
author: Christopher A. H. Paul
author: David R. Willé
published in: Advances in Computational Mathematics
publication date: 1995-10-09T00:00:00Z
review text: This is a comprehensive survey article on the numerical treatment of delay differential equations. It starts with some simple examples and with analytical properties: step by step solution, qualitative properties, stability, and propagation of discontinuities. Then, the following numerical issues are discussed: use of dense output, numerical stability and order, choice between multistep and Runge-Kutta methods, tracking discontinuities, treatment of vanishing lag. It concludes with a list of 95 references.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 803472
zbMATH Keywords: survey article
zbMATH Keywords: delay differential equations
zbMATH Keywords: stability
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: discontinuities
describes a project that uses: DELSOL
describes a project that uses: Matlab
MaRDI profile type: Publication
cites work: Numerical solution of retarded initial value problems: Local and global error and stepsize control
cites work: Q5522536
cites work: The Numerical Solution of Delay-Differential-Algebraic Equations of Retarded and Neutral Type
cites work: Propositions on the robustness of multistep formulae
cites work: Q3837479
cites work: Computing stability regions—Runge-Kutta methods for delay differential equations
cites work: Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations
cites work: Spline approximations for functional differential equations
cites work: Special stability problems for functional differential equations
cites work: One-step collocation for delay differential equations
cites work: Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method
cites work: Differential-difference equations
cites work: Q5829378
cites work: Numerical integration of a differential-difference equation with a decreasing time-lag
cites work: Q3939135
cites work: Stepsize control for delay differential equations using a pair of formulae
cites work: Q4846444
cites work: An implementation of singly-implicit Runge-Kutta methods
cites work: The adaptation of STRIDE to delay differential equations
cites work: NUMERICAL METHODS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS
cites work: Ordinary and delay differential equations
cites work: Q5343704
cites work: Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
cites work: Q3837480
cites work: The Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge–Kutta Formulas
cites work: A new error-control for initial value solvers
cites work: Analysis of Error Control Strategies for Continuous Runge–Kutta Methods
cites work: Interpolating Runge-Kutta methods for vanishing delay differential equations
cites work: Interpolants for Runge-Kutta formulas
cites work: High Order Methods for State-Dependent Delay Differential Equations with Nonsmooth Solutions
cites work: Numerical Methods for Nonlinear Volterra Integro-Differential Equations
cites work: Q4003237
cites work: Q3550030
cites work: Differential equations: Stability, oscillations, time lags
cites work: Highly continuous Runge-Kutta interpolants
cites work: A new class of one-step methods for the solution of Volterra functional differential equations
cites work: The stability of a class of Runge-Kutta methods for delay differential equations
cites work: A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
cites work: Stability analysis of numerical methods for delay differential equations
cites work: Linear Multistep Methods with Reduced Truncation Error for Periodic Initial-value Problems
cites work: Stability in linear multistep methods for pure delay equations
cites work: On the Stability of Predictor-Corrector Methods for Parabolic Equations with Delay
cites work: Stability and Dynamics of Numerical Methods for Nonlinear Ordinary Differential Equations
cites work: Stability of the Discretized Pantograph Differential Equation
cites work: The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods
cites work: Spline Approximations for Neutral Functional Differential Equations
cites work: ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE FUNCTIONAL DIFFERENTIAL EQUATION y′(x) = ay(λx) + by(x)
cites work: The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$
cites work: Q3137918
cites work: Stability of functional differential equations
cites work: Linear Multistep Methods for Volterra Integro-Differential Equations
cites work: Delay differential equations: with applications in population dynamics
cites work: The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
cites work: Automatic Integration of Functional Differential Equations: An Approach
cites work: Software for the numerical solution of systems of functional differential equations with state-dependent delays
cites work: Characterization of jump discontinuities for state dependent delay differential equations

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cites work: Numerical treatment of delay differential equations by Hermite interpolation

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cites work: Q4151670

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cites work: Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods

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cites work: Developing a delay differential equation solver

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cites work: Q5527119

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cites work: Interpolation for Runge–Kutta Methods

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cites work: The Effect of Changing the Stepsize in Linear Multistep Codes

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cites work: Slowly oscillating periodic solutions of autonomous state-dependent delay equations

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cites work: Q5610717

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cites work: One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations

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cites work: Stability of numerical methods for delay differential equations

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cites work: Stability of Multistep Methods for Delay Differential Equations

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cites work: Experiments in stepsize control for Adams linear multistep methods

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cites work: Stepsize control and continuity consistency for state-dependent delay- differential equations

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cites work: The tracking of derivative discontinuities in systems of delay- differential equations

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cites work: DELSOL -- a numerical code for the solution of systems of delay- differential equations

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cites work: Natural Continuous Extensions of Runge-Kutta Methods

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cites work: P-stability properties of Runge-Kutta methods for delay differential equations

Issues in the numerical solution of evolutionary delay differential equations (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02988625

Issues in the numerical solution of evolutionary delay differential equations (OpenAlex ID)
OpenAlex ID: W4246289621