### 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) |
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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 |
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City | Austin, TX, USA |

Period | 12/7/88 → 12/9/88 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

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

*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.

}

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.

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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 -