### 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 |

Publication status | 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 |

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### 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.