Fully implicit one-step methods for neutral functional-differential equations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The author discusses the class of fully implicit one-step methods of any order for the numerical solution of neutral functional-differential equations. For judicious choices of the parameters these methods are NP-stable, which means that the numerical approximation to the solution Y of the linear test equation y′ = ay(t) + by(t-d) + cy′(t-d), t ≥ 0, is bounded whenever Y is bounded. This property is an analogue of A-stability of ordinary differential equations. The local discretization error of these methods can be estimated by comparing two approximations of successive orders. This can be done in a very efficient way, and these methods can be implemented in variable-step mode with a step-changing strategy based on this estimate. Numerical results are presented that illustrate the high potential of fully implicit formulas.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Pages813
Number of pages1
StatePublished - Dec 1988
EventProceedings of the 27th IEEE Conference on Decision and Control - Austin, TX, USA
Duration: Dec 7 1988Dec 9 1988

Other

OtherProceedings of the 27th IEEE Conference on Decision and Control
CityAustin, TX, USA
Period12/7/8812/9/88

Fingerprint

Ordinary differential equations
Differential equations

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

Cite this

Jackiewicz, Z. (1988). Fully implicit one-step methods for neutral functional-differential equations. In Proceedings of the IEEE Conference on Decision and Control (pp. 813). Publ by IEEE.

Fully implicit one-step methods for neutral functional-differential equations. / Jackiewicz, Zdzislaw.

Proceedings of the IEEE Conference on Decision and Control. Publ by IEEE, 1988. p. 813.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jackiewicz, Z 1988, Fully implicit one-step methods for neutral functional-differential equations. in Proceedings of the IEEE Conference on Decision and Control. Publ by IEEE, pp. 813, Proceedings of the 27th IEEE Conference on Decision and Control, Austin, TX, USA, 12/7/88.
Jackiewicz Z. Fully implicit one-step methods for neutral functional-differential equations. In Proceedings of the IEEE Conference on Decision and Control. Publ by IEEE. 1988. p. 813
Jackiewicz, Zdzislaw. / Fully implicit one-step methods for neutral functional-differential equations. Proceedings of the IEEE Conference on Decision and Control. Publ by IEEE, 1988. pp. 813
@inproceedings{57d4aa08a0bb4c7f9f2568e3cbbf5905,
title = "Fully implicit one-step methods for neutral functional-differential equations",
abstract = "The author discusses the class of fully implicit one-step methods of any order for the numerical solution of neutral functional-differential equations. For judicious choices of the parameters these methods are NP-stable, which means that the numerical approximation to the solution Y of the linear test equation y′ = ay(t) + by(t-d) + cy′(t-d), t ≥ 0, is bounded whenever Y is bounded. This property is an analogue of A-stability of ordinary differential equations. The local discretization error of these methods can be estimated by comparing two approximations of successive orders. This can be done in a very efficient way, and these methods can be implemented in variable-step mode with a step-changing strategy based on this estimate. Numerical results are presented that illustrate the high potential of fully implicit formulas.",
author = "Zdzislaw Jackiewicz",
year = "1988",
month = "12",
language = "English (US)",
pages = "813",
booktitle = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Publ by IEEE",

}

TY - GEN

T1 - Fully implicit one-step methods for neutral functional-differential equations

AU - Jackiewicz, Zdzislaw

PY - 1988/12

Y1 - 1988/12

N2 - The author discusses the class of fully implicit one-step methods of any order for the numerical solution of neutral functional-differential equations. For judicious choices of the parameters these methods are NP-stable, which means that the numerical approximation to the solution Y of the linear test equation y′ = ay(t) + by(t-d) + cy′(t-d), t ≥ 0, is bounded whenever Y is bounded. This property is an analogue of A-stability of ordinary differential equations. The local discretization error of these methods can be estimated by comparing two approximations of successive orders. This can be done in a very efficient way, and these methods can be implemented in variable-step mode with a step-changing strategy based on this estimate. Numerical results are presented that illustrate the high potential of fully implicit formulas.

AB - The author discusses the class of fully implicit one-step methods of any order for the numerical solution of neutral functional-differential equations. For judicious choices of the parameters these methods are NP-stable, which means that the numerical approximation to the solution Y of the linear test equation y′ = ay(t) + by(t-d) + cy′(t-d), t ≥ 0, is bounded whenever Y is bounded. This property is an analogue of A-stability of ordinary differential equations. The local discretization error of these methods can be estimated by comparing two approximations of successive orders. This can be done in a very efficient way, and these methods can be implemented in variable-step mode with a step-changing strategy based on this estimate. Numerical results are presented that illustrate the high potential of fully implicit formulas.

UR - http://www.scopus.com/inward/record.url?scp=0024171664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024171664&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0024171664

SP - 813

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

ER -