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On perturbed trapezoidal and midpoint rules

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Abstract

Explicit bounds are obtained for the perturbed, or corrected, trapezoidal and midpoint rules in terms of the Lebesque norms of the second derivative of the function. It is demonstrated that the bounds obtained are the same for both rules although the perturbation or the correction term is different.

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References

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  2. N.S. Barnett and S.S. Dragomir,On the perturbed trapezoid formula, Preprint: RGMIA Res. Rep. Coll.,4 (2), Article 6, 2001. [ONLINE]http://rgmia.vu.edu.au/v4n2.html

  3. N.S. Barnett, P. Cerone and S.S. Dragomir,A sharp bound for the error in the corrected trapezoid rule and applications, submitted.

  4. P. Cerone,On relationships between Ostrowski, trapezoidal and Chebychev identities and inequalities, Preprint:RGMIA Res. Rep. Coll.,4(2), Article 14, 2001. [ONLINE]http: //rgmia. vu. edu. au/v4n2. html

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Authors and Affiliations

  1. School of Communications and Informatics, Victoria University of Technology, Melbourne City MC, PO Box 14428, 8001, Victoria, Australia

    P. Cerone

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  1. P. Cerone
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Cerone, P. On perturbed trapezoidal and midpoint rules. Korean J. Comput. & Appl. Math. 9, 423–435 (2002). https://doi.org/10.1007/BF03021551

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  • DOI: https://doi.org/10.1007/BF03021551

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