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

Zdzislaw Jackiewicz

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

Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

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 language	English (US)
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	Publ by IEEE
Pages	813
Number of pages	1
State	Published - Dec 1988
Event	Proceedings of the 27th IEEE Conference on Decision and Control - Austin, TX, USA Duration: Dec 7 1988 → Dec 9 1988

Other

Other	Proceedings of the 27th IEEE Conference on Decision and Control
City	Austin, TX, USA
Period	12/7/88 → 12/9/88

ASJC Scopus subject areas

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

Cite this

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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.",

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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.

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M3 - Conference contribution

AN - SCOPUS:0024171664

SP - 813

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 27th IEEE Conference on Decision and Control

Y2 - 7 December 1988 through 9 December 1988

ER -

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

Abstract

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ASJC Scopus subject areas

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