Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON PERTURBED TRAPEZOIDAL AND MIDPOINT RULES

  • Cerone, P. (School of Communications and Informatics, Victoria University of Technology)
  • Published : 2002.05.01

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Abstract

Explicit hounds 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.

Keywords

References

  1. An Introduction to Numerical Analysis(Second Edition) K. E. Atkinson
  2. RGMIA Res. Rep. Coll. v.4 no.2 On the perturbed trapezoid formula N. S. Barnett;S. S. Dragomir
  3. A sharp bound for the error in the corrected trapezoid rule and applications, submitted N. S. Barnett;P. Cerone;S. S. Dragomir
  4. RGMIA Res. Rep. Coll. v.4 no.2 On relationships between Ostrowski, trapezoidal and Chebychev identities and inequalities P. Cerone
  5. Theory of Inequalities and Applications Perturbed rules in numerical integration from product branched Peano kernels P. Cerone;Y. J. Cho(Ed.);S. S. Dragomir(Ed.);J.K. Kim(Ed.)
  6. Acepted for publication in Analytic-Computational Methods in Applied Mathematics Midpoint type rules from an inequalities point of view P. Cerone;S. S. dragomir;G. A. Anastassiou(Ed)
  7. Accepted for publication in Analytic-Computational Methods in Applied Mathematics Trapezoidal type rules from an inequalities point of view P. Cerone;S. S. Dragomir;G. A. Anastassiou(Ed)
  8. Some remarks on the midpoint rule in numerical integration, submitted S. S. Dragomir;P. Cerone;A. Sofo
  9. Indian J. of Pure and Appl. Math. Some remarks on the trapezoid rule in numerical integration S. S. Dragomir;P. Cerone;A. Sofo
  10. Preprint: RGMIA Res. Rep. Coll. v.2 no.5 S. S. Dragomir;P. Cerone;A. Sofo
  11. Classical and New Inequalities in Analysis D. S. Mitrinovic;J. E. Pecaric;A. M. Fink