Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations
type: Item
instance of: scholarly article
title: Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations
zbMATH Open document ID: 0626.65072
DOI: 10.1016/0168-9274(87)90036-5
published in: Applied Numerical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A variable-step algorithm of variable order is developed for the numerical solution of neutral functional-differential equations of the form \[ y'(t)=f(t,y(\cdot),y'(\cdot),\quad t\in [a,b],\quad y(t)=g(t),\quad t\in [\gamma,a] \] where \(\gamma \leq a<b\). The algorithm is based on a predictor-corrector method with automatic control of step size and order. Although the error estimates are valid only under strong hypotheses, several numerical experiments indicate that the algorithm can be both accurate and efficient for neutral equations with variable delays under less stringent conditions. In the case of functional differential equations not of neutral type, further improvement of efficiency can be obtained by modifying the algorithm.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 4018271
zbMATH Keywords: Adams methods
zbMATH Keywords: variable stepsize variable order method
zbMATH Keywords: automatic stepsize control
zbMATH Keywords: numerical examples
zbMATH Keywords: neutral functional-differential equations
zbMATH Keywords: predictor-corrector method
zbMATH Keywords: error estimates
zbMATH Keywords: equations with variable delays
author: Zdzislaw Jackiewicz
MaRDI profile type: Publication
full work available at URL: 0168-9274(87)90036-5
OpenAlex ID: W2026791915
cites work: Q3661894
cites work: Q4745219
cites work: Numerical solution of retarded initial value problems: Local and global error and stepsize control
cites work: On the computational solution of differential-difference equations
cites work: Numerical integration of a differential-difference equation with a decreasing time-lag
cites work: On the computational solution of a class of functional differential equations
cites work: Q5728644
cites work: Existence and continuous dependence of solutions of a neutral functional- differential equation
cites work: Q3331569
cites work: Existence and Continuous Dependence for a Class of Nonlinear Neutral- Differential Equations
cites work: Numerical Methods for Nonlinear Volterra Integro-Differential Equations
cites work: High Order Methods for State-Dependent Delay Differential Equations with Nonsmooth Solutions
cites work: Theory of functional differential equations. 2nd ed
cites work: A problem in the theory of epidemics
cites work: One-Step Methods of any Order for Neutral Functional Differential Equations
cites work: Quasilinear Multistep Methods and Variable Step Predictor–Corrector Methods for Neutral Functional-Differential Equations
cites work: Q3767626
cites work: Q3985594
cites work: On the Cauchy Problem for Differential-Delay Equations in a Banach Space
cites work: Spline Approximations for Neutral Functional Differential Equations
cites work: Numerical solution of ordinary differential equations
cites work: Automatic Integration of Functional Differential Equations: An Approach
cites work: Algorithm 497: Automatic Integration of Functional Differential Equations [D2]
cites work: Control of Interpolatory Error in Retarded Differential Equations
cites work: Characterization of jump discontinuities for state dependent delay differential equations
cites work: Numerical treatment of delay differential equations by Hermite interpolation
cites work: Q4151670
cites work: Q4117285
description: scientific article; zbMATH DE number 4018271