# A corrected quadrature formula and applications

Article

*Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal.*45 (E), pp. E41-E56.

Article Title | A corrected quadrature formula and applications |
---|---|

ERA Journal ID | 43 |

Article Category | Article |

Authors | Ujevic, Nenad (Author) and Roberts, A. J. (Author) |

Journal Title | Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal |

Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal | |

Journal Citation | 45 (E), pp. E41-E56 |

Year | 2004 |

Place of Publication | Australia |

ISSN | 1446-1811 |

1446-8735 | |

Web Address (URL) | http://anziamj.austms.org.au/V45/E051/Nenad.pdf |

Abstract | [Abstract]: A straightforward three-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives. |

Keywords | quadrature formula |

ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |

Public Notes | There are no files associated with this item. |

Byline Affiliations | University of Split, Croatia |

Department of Mathematics and Computing |

https://research.usq.edu.au/item/9y53q/a-corrected-quadrature-formula-and-applications

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