Numerical solution of neutral functional differential equations by Adams methods in divided difference form
type: Item
instance of: scholarly article
title: Numerical solution of neutral functional differential equations by Adams methods in divided difference form
zbMATH Open document ID: 1090.65084
author: N. E. Zubov
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: An algorithm of variable step and variable order for the numerical solution of neutral functional differential equations (NFDE) is described. The form of NFDE are: \[ \begin{aligned} y'(t) &= f\bigl(t,y(\bullet),y'(\bullet)\bigr), \;t\in[a,b]\\ y(t)& =g(t),\;t\in[\tau,\alpha],\;y'(t)=g'(t),\;t\in[\tau,\alpha] \end{aligned} \] with \(\tau\leq\alpha<b\) and \(g\in C_n^1[\tau,\alpha]\) is a given initial function. The algorithm for the solution of the above system is based on the variable step formulation of the Adams methods represented in divided difference form in which the Adams-Bashforth and Adams-Moulton methods are implemented in predictor-corrector mode. The restarting of the integration at each discontinuity point (derivative discontinuities) relies on the step size and order changing strategy based on the estimates of the local discretization errors. The algorithm reduces the computational cost and increases the reliability and efficiency by obtaining asymptotically correct estimates of the local discretization errors. The method is tested in three test examples.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 5015155
zbMATH Keywords: variable step
zbMATH Keywords: variable order
zbMATH Keywords: Adams methods
zbMATH Keywords: divided difference form
zbMATH Keywords: neutral functional differential equations
zbMATH Keywords: predictor-corrector mode
zbMATH Keywords: step size and order changing strategy
zbMATH Keywords: Adams-Bashforth method
zbMATH Keywords: numerical examples
zbMATH Keywords: error estimates
zbMATH Keywords: algorithm
zbMATH Keywords: Adams-Moulton methods
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
full work available at URL: j.cam.2005.02.016
OpenAlex ID: W2021829913
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DOI: 10.1016/J.CAM.2005.02.016
description: scientific article; zbMATH DE number 5015155