# Asymptotic expressions for remainder terms of some quadrature rules

Open Mathematics (2008)

- Volume: 6, Issue: 4, page 559-567
- ISSN: 2391-5455

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topNenad Ujević, and Nataša Bilić. "Asymptotic expressions for remainder terms of some quadrature rules." Open Mathematics 6.4 (2008): 559-567. <http://eudml.org/doc/269515>.

@article{NenadUjević2008,

abstract = {Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.},

author = {Nenad Ujević, Nataša Bilić},

journal = {Open Mathematics},

keywords = {quadrature rules; error terms; asymptotic expressions; asymptotic expansions; remainder terms; mid-point; trapezoid and Simpson's rules},

language = {eng},

number = {4},

pages = {559-567},

title = {Asymptotic expressions for remainder terms of some quadrature rules},

url = {http://eudml.org/doc/269515},

volume = {6},

year = {2008},

}

TY - JOUR

AU - Nenad Ujević

AU - Nataša Bilić

TI - Asymptotic expressions for remainder terms of some quadrature rules

JO - Open Mathematics

PY - 2008

VL - 6

IS - 4

SP - 559

EP - 567

AB - Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.

LA - eng

KW - quadrature rules; error terms; asymptotic expressions; asymptotic expansions; remainder terms; mid-point; trapezoid and Simpson's rules

UR - http://eudml.org/doc/269515

ER -

## References

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- [2] Cerone P., Dragomir S.S., Midpoint-type rules from an inequalities point of view, In: Handbook of analyticcomputational methods in applied mathematics, Anastassiou G. (Ed.), CRC Press, New York, 2000, 135–200 Zbl0966.26015
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- [7] Dragomir S.S., Rassias Th.M., Ostrowski type inequalities and applications in numerical integration, Kluwer Academic, 2002
- [8] Krommer A.R., Ueberhuber C.W., Computational integration, SIAM, Philadelphia, 1998 Zbl0903.65019
- [9] Pearce C.E.M., Pečarić J., Ujevic N., Varosanec S., Generalizations of some inequalities of Ostrowski-Gross type, Math. Inequal. Appl., 2000, 3, 25–34 Zbl0978.26011
- [10] Ujevic N., On perturbed mid-point and trapezoid inequalities and applications, Kyungpook Math. J., 2003, 43, 327–334 Zbl1034.26023
- [11] Ujevic N., A generalization of Ostrowski’s inequality and applications in numerical integration, Appl. Math. Lett., 2004, 17, 133–137 http://dx.doi.org/10.1016/S0893-9659(04)90023-7 Zbl1057.26023
- [12] Ujevic N., Roberts A.J., A corrected quadrature formula and applications, ANZIAM J., 2003, 45, 41–56 Zbl1076.41017
- [13] Whittaker E.T., Watson G.N., A course of modern analysis, Cambridge, 1996

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