### Abstract

A new numerical algorithm is presented for the solution to the point kinetics equations (PKEs), whose accurate solution has been sought for over 60 years. The method couples the simplest of finite difference methods, a backward Euler, with Richardsons extrapolation, also called an acceleration. From this coupling, a series of benchmarks have emerged. These include cases from the literature as well as several new ones. The novelty of this presentation lies in the breadth of reactivity insertions considered, covering both prescribed and feedback reactivities, and the extreme 8- to 9- digit accuracy achievable. The benchmarks presented are to provide guidance to those who wish to develop further numerical improvements.

Original language | English (US) |
---|---|

Title of host publication | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 |

Pages | 2119-2146 |

Number of pages | 28 |

Volume | 3 |

Publication status | Published - 2013 |

Externally published | Yes |

Event | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 - Sun Valley, ID, United States Duration: May 5 2013 → May 9 2013 |

### Other

Other | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 |
---|---|

Country | United States |

City | Sun Valley, ID |

Period | 5/5/13 → 5/9/13 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear Energy and Engineering
- Applied Mathematics

### Cite this

*International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013*(Vol. 3, pp. 2119-2146)