Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
type: Item
instance of: scholarly article
title: Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
zbMATH Open document ID: 0876.65089
DOI: 10.1016/S0168-9274(97)00019-6
author: W. H. Enright
author: Min Hu
published in: Applied Numerical Mathematics
publication date: 1997-11-11T00:00:00Z
review text: Explicit and implicit continuous Runge-Kutta methods (i.e., Runge-Kutta methods with dense output) are used for the numerical treatment of neutral Volterra integro-differential equations with delay. The order of convergence is investigated and it is shown that the arising nonlinear systems can be solved by fixed point iteration as long as the considered problem is non-stiff. A few numerical experiments are included.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 1036652
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: dense output
zbMATH Keywords: neutral Volterra integro-differential equations
zbMATH Keywords: delay equations
zbMATH Keywords: convergence
zbMATH Keywords: fixed point iteration
zbMATH Keywords: numerical experiments
reviewed by: Ernst Hairer
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations
cites work: Stability analysis of one-step methods for neutral delay-differential equations
cites work: Q4839882
cites work: Q3750978
cites work: The Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge–Kutta Formulas
cites work: Convergence Analysis of the Solution of Retarded and Neutral Delay Differential Equations by Continuous Numerical Methods
cites work: Solving Ordinary Differential Equations I
cites work: Q4000061
cites work: One-Step Methods of any Order for Neutral Functional Differential Equations
cites work: The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods
cites work: On the Cauchy Problem for Differential-Delay Equations in a Banach Space
cites work: Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations
full work available at URL: s0168-9274(97)00019-6
OpenAlex ID: W2037658016
description: scientific article; zbMATH DE number 1036652