A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
type: Item
instance of: scholarly article
title: A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
zbMATH Open document ID: 0765.65069
DOI: 10.1007/BF01994847
author: Karel J. in 't Hout
published in: BIT
publication date: 1993-01-26T00:00:00Z
review text: The numerical solution of the initial value problem for delay- differential equations \(x'(t)=f(t,x(t),x(t-\tau))\), \(t\geq 0\), \(x(t)=g(t)\), \(t\leq 0\) is considered. A new interpolation procedure is introduced which leads to numerical processes that satisfy an asymptotic stability condition related to the class of test problems \(x'(t)=\lambda x(t)+\mu x(t-\tau)\) with \(\lambda\) and \(\mu\in\mathbb{C}\), \(\text{Re}(\lambda)<-|\mu|\) and \(\tau>0\).
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 86147
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: initial value problem
zbMATH Keywords: delay-differential equations
zbMATH Keywords: interpolation procedure
zbMATH Keywords: asymptotic stability condition
zbMATH Keywords: test problem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01994847
OpenAlex ID: W2036663938
description: scientific article; zbMATH DE number 86147