On the discretization of differential and Volterra integral equations with variable delay
type: Item
instance of: scholarly article
title: On the discretization of differential and Volterra integral equations with variable delay
zbMATH Open document ID: 0873.65126
DOI: 10.1007/BF02510168
author: H. Brunner
published in: BIT
publication date: 1997-10-16T00:00:00Z
review text: This paper deals with discretization techniques applied to differential and Volterra integral equations of the second kind with variable delay. Collocation and iterated collocation methods are used for solving these equations and the problem of the attainable order of \(m\)-stage implicit Runge-Kutta methods with variable delays (of the form \(qt\), \(0< q< 1)\) is studied. It is proved that, in contrast to equations without delay, or equations with constant delay, collocation at the Gauss (-Legendre) points will no longer yield the optimal (local) order \(O(h^{2m})\). A numerical linear example is given.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 1000359
zbMATH Keywords: collocation
zbMATH Keywords: numerical example
zbMATH Keywords: Volterra integral equations
zbMATH Keywords: variable delay
zbMATH Keywords: implicit Runge-Kutta methods
reviewed by: Yves Cherruault
describes a project that uses: RODAS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1000359