The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

An algorithm for the numerical solution of neutral functional‐differential equations is described. This algorithm is based on divided difference representation of fully implicit one‐step methods. The resulting systems of nonlinear equations are solved using the predictor‐corrector approach for nonstiff equations and by the modified Newton method for stiff equations. The step control strategy is based on local error estimation by comparing two approximations of successive orders. The details of implementations are described for systems of neutral delay‐differential equations with state dependent delays, for Volterra integro‐differential equations and for stiff delay‐differential equations. The results of some numerical experiments on four test examples are presented and discussed.

Original languageEnglish (US)
Pages (from-to)207-221
Number of pages15
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume75
Issue number3
DOIs
StatePublished - 1995

Fingerprint

Stiff Equations
Neutral Equation
Implicit Method
Delay Differential Equations
Numerical integration
Local Error Estimation
Modified Newton Method
State-dependent Delay
Volterra Integro-differential Equations
Divided Differences
Integrodifferential equations
System of Nonlinear Equations
Newton-Raphson method
Nonlinear equations
Error analysis
Control Strategy
Numerical Experiment
Numerical Solution
Approximation
Experiments

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

Cite this

@article{5afb2cf14a38446aac7d866ffd333f2b,
title = "The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods",
abstract = "An algorithm for the numerical solution of neutral functional‐differential equations is described. This algorithm is based on divided difference representation of fully implicit one‐step methods. The resulting systems of nonlinear equations are solved using the predictor‐corrector approach for nonstiff equations and by the modified Newton method for stiff equations. The step control strategy is based on local error estimation by comparing two approximations of successive orders. The details of implementations are described for systems of neutral delay‐differential equations with state dependent delays, for Volterra integro‐differential equations and for stiff delay‐differential equations. The results of some numerical experiments on four test examples are presented and discussed.",
author = "Zdzislaw Jackiewicz and E. Lo",
year = "1995",
doi = "10.1002/zamm.19950750308",
language = "English (US)",
volume = "75",
pages = "207--221",
journal = "ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik",
issn = "0044-2267",
publisher = "Wiley-VCH Verlag",
number = "3",

}

TY - JOUR

T1 - The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods

AU - Jackiewicz, Zdzislaw

AU - Lo, E.

PY - 1995

Y1 - 1995

N2 - An algorithm for the numerical solution of neutral functional‐differential equations is described. This algorithm is based on divided difference representation of fully implicit one‐step methods. The resulting systems of nonlinear equations are solved using the predictor‐corrector approach for nonstiff equations and by the modified Newton method for stiff equations. The step control strategy is based on local error estimation by comparing two approximations of successive orders. The details of implementations are described for systems of neutral delay‐differential equations with state dependent delays, for Volterra integro‐differential equations and for stiff delay‐differential equations. The results of some numerical experiments on four test examples are presented and discussed.

AB - An algorithm for the numerical solution of neutral functional‐differential equations is described. This algorithm is based on divided difference representation of fully implicit one‐step methods. The resulting systems of nonlinear equations are solved using the predictor‐corrector approach for nonstiff equations and by the modified Newton method for stiff equations. The step control strategy is based on local error estimation by comparing two approximations of successive orders. The details of implementations are described for systems of neutral delay‐differential equations with state dependent delays, for Volterra integro‐differential equations and for stiff delay‐differential equations. The results of some numerical experiments on four test examples are presented and discussed.

UR - http://www.scopus.com/inward/record.url?scp=84983991453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983991453&partnerID=8YFLogxK

U2 - 10.1002/zamm.19950750308

DO - 10.1002/zamm.19950750308

M3 - Article

AN - SCOPUS:84983991453

VL - 75

SP - 207

EP - 221

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 3

ER -