### Abstract

The burnup equations can in principle be solved by
computing the exponential of the burnup matrix. However,
due to the difficult numerical characteristics of burnup
matrices, the problem is extremely stiff and the matrix
exponential solution has previously been considered
infeasible for an entire burnup system containing over a
thousand nuclides. It was recently discovered by the
author that the eigenvalues of burnup matrices are
generally located near the negative real axis, which
prompted introducing the Chebyshev rational approximation
method (CRAM) for solving the burnup equations. CRAM can
be characterized as the best rational approximation on
the negative real axis and it has been shown to be
capable of simultaneously solving an entire burnup system
both accurately and efficiently. In this paper, the
accuracy of CRAM is further studied in the context of
burnup equations. The approximation error is analyzed
based on the eigenvalue decomposition of the burnup
matrix. It is deduced that the relative accuracy of CRAM
may be compromised if a nuclide concentration diminishes
significantly during the considered time step. Numerical
results are presented for two test cases, the first one
representing a small burnup system with 36 nuclides and
the second one a full a decay system with 1531 nuclides.

Original language | English |
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Title of host publication | Proceedings |

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

Pages | 973-984 |

Publication status | Published - 2013 |

MoE publication type | Not Eligible |

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

### Conference

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

Abbreviated title | M&C 2013 |

Country | United States |

City | Sun Valley, ID |

Period | 5/05/13 → 9/05/13 |

### Keywords

- best rational approximation
- burnup equations
- CRAM
- serpent

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## Cite this

Pusa, M. (2013). Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. In

*Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013*(pp. 973-984)