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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 239695, 9 pages
Some New Estimates for the Error of Simpson Integration Rule
1Department of Mathematics, K. N. Toosi University of Technology, Tehran 19697, Iran
2Department of Mathematics, King AbdulAziz University, Jeddah 21589, Saudi Arabia
Received 9 September 2012; Accepted 10 October 2012
Academic Editor: Mohammad Mursaleen
Copyright © 2012 Mohammad Masjed-Jamei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- W. Gautschi, Numerical Analysis: An Introduction, Birkhäuser, Boston, Mass, USA, 1997.
- P. Cerone, “Three points rules in numerical integration,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 4, pp. 2341–2352, 2001.
- D. Cruz-Uribe and C. J. Neugebauer, “Sharp error bounds for the trapezoidal rule and Simpson's rule,” Journal of Inequalities in Pure and Applied Mathematics, vol. 3, no. 4, article 49, pp. 1–22, 2002.
- S. S. Dragomir, R. P. Agarwal, and P. Cerone, “On Simpson's inequality and applications,” Journal of Inequalities and Applications, vol. 5, no. 6, pp. 533–579, 2000.
- S. S. Dragomir, P. Cerone, and J. Roumeliotis, “A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means,” Applied Mathematics Letters, vol. 13, no. 1, pp. 19–25, 2000.
- S. S. Dragomir, J. Pečarić, and S. Wang, “The unified treatment of trapezoid, Simpson, and Ostrowski type inequality for monotonic mappings and applications,” Mathematical and Computer Modelling, vol. 31, no. 6-7, pp. 61–70, 2000.
- I. Fedotov and S. S. Dragomir, “An inequality of Ostrowski type and its applications for Simpson's rule and special means,” Mathematical Inequalities & Applications, vol. 2, no. 4, pp. 491–499, 1999.
- M. Masjed-Jamei, “A linear constructive approximation for integrable functions and a parametric quadrature model based on a generalization of Ostrowski-Grüss type inequalities,” Electronic Transactions on Numerical Analysis, vol. 38, pp. 218–232, 2011.
- M. Matić, “Improvement of some inequalities of Euler-Grüss type,” Computers & Mathematics with Applications, vol. 46, no. 8-9, pp. 1325–1336, 2003.
- N. Ujević, “New error bounds for the Simpson's quadrature rule and applications,” Computers & Mathematics with Applications, vol. 53, no. 1, pp. 64–72, 2007.