A corrected quadrature formula and applications
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2003
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| Subjects: | |
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| _version_ | 1866915560146599936 |
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| author | Ujevic, Nenad Roberts, A. J. |
| author_facet | Ujevic, Nenad Roberts, A. J. |
| contents | A straightforward 3-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0303342 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | A corrected quadrature formula and applications Ujevic, Nenad Roberts, A. J. Numerical Analysis A straightforward 3-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. |
| title | A corrected quadrature formula and applications |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0303342 |