# Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations

Research output: Contribution to journalArticle

9 Citations (Scopus)

### Abstract

The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.

Original language English (US) 317-329 13 Applied Numerical Mathematics 3 4 https://doi.org/10.1016/0168-9274(87)90036-5 Published - 1987 Yes

### Fingerprint

Neutral Functional Differential Equation
Differential equations
Numerical Solution
Interpolation
Interpolate
Predictor-corrector Methods
Discretization Error
Numerical Experiment
Formulation
Estimate
Experiments

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Modeling and Simulation

### Cite this

In: Applied Numerical Mathematics, Vol. 3, No. 4, 1987, p. 317-329.

Research output: Contribution to journalArticle

@article{c85b9a6ee8614ed18faefff0f65c96f7,
title = "Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations",
abstract = "The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.",
author = "Zdzislaw Jackiewicz",
year = "1987",
doi = "10.1016/0168-9274(87)90036-5",
language = "English (US)",
volume = "3",
pages = "317--329",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations

AU - Jackiewicz, Zdzislaw

PY - 1987

Y1 - 1987

N2 - The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.

AB - The variable-step variable-order algorithm based on predictor-corrector methods for neutral functional differential equations is described. The algorithm is implemented in interpolation mode, i.e. we use fixed-step formulation of Adams-Bashford Adams-Moulton formulas while all back-values are computed by interpolation. The local discretization error is estimated by Milne's device. Although the assumptions under which this estimate is asymptotically correct are rather strong and not always expected to be satisfied in practice, the numerical experiments up to date indicate that this algorithm can be quite accurate and efficient.

UR - http://www.scopus.com/inward/record.url?scp=0023394087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023394087&partnerID=8YFLogxK

U2 - 10.1016/0168-9274(87)90036-5

DO - 10.1016/0168-9274(87)90036-5

M3 - Article

AN - SCOPUS:0023394087

VL - 3

SP - 317

EP - 329

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 4

ER -