Open Newton-Cotes Quadrature with Midpoint Derivative

Authors

  • Dr. Kaushal Rana Assistant Professor, Department of Mathematics, Dau Dayal Institute of Vocational Education, Dr Bhimrao Ambedkar University, Agra, Uttar Pradesh, INDIA.

Keywords:

ONC formulas, Newton cotes formulas

Abstract

In this paper, as a new approach arithmetic mean of end points is applied at the error term derivative in the existing ONC formulas. The new error terms are also derived by applying the method of precision. This arithmetic mean derivative based ONC formulas increase the two orders of precision than the previous ONC formulas and the left out statistical means are the scope for future studies in the ONC formulas.  

References

Weijing Zhao and Hongxing, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Abstract and Applied Analysis, Article ID 492507, 10 pages, 2013.

K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, USA, 2nd edition, 1989.

R. L. Burden and J. D. Faires, Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.

E. Isaacson and H. B. Keller, Analysis of Numerical Methods, JohnWiley & Sons, New York, USA, 1966.

F.Hildebrand, Introduction to Numerical Analysis, Dover publications, New York, 1974.

J. Stoer and R. Bulirsch, , Introduction to Numerical Analysis, Springer, 1992.

W. Zhu, X. Zhao, and Y. Tang, Numerical methods with a high order of accuracy applied in the quantum system, Journal of Chemical Physics, Vol. 104, no. 6, pp.2275–2286, 1996.

J. C. Chiou and S. D.Wu, Open Newton-Cotes differential methods as multilayer symplectic integrators, Journal of Chemical Physics, Vol. 107, no. 17, pp. 6894–6898, 1997.

G. Vanden Berghe and M. Van Daele, Exponentially fitted open Newton–Cotes differential methods as multilayer symplectic integrators, The Journal of Chemical Physics 132, 2010.

T. E. Simos, New open modified trigonometrically-fitted Newton-Cotes type multilayer symplectic integrators for the numerical solution of the Schrödinger equation, J Math. Chem. 50, pp. 782–804, 2012.

G. H. Ibraheem, Solving System of Linear Fredholm Integral Equations of Second Kind Using Open Newton-Cotes Formulas, IBN AL- Haitham J. For Pure & Appl. Sci., Vol.24 (2), 2011.

M. Dehghan, M. Masjed-Jamei and M.R. Eslahchi, On numerical improvement of open Newton–Cotes quadrature rules, Applied Mathematics and Computation 175 , pp.618–627,2006.

Clarence O.E.Burg and Ezechiel Degny, Derivative-Based midpoint quadrature rule, Applied mathematics, Vol.4, pp. 228- 234, 2013.

Fiza Zafar, Saira Saleem and Clarence O.E.Burg, New Derivative based open Newton-cotes quadrature rules, Abstract and Applied Analysis, Article ID 109138, 16 pages, 2014.

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Published

2022-06-05

How to Cite

Kaushal Rana. (2022). Open Newton-Cotes Quadrature with Midpoint Derivative. Stallion Journal for Multidisciplinary Associated Research Studies, 1(3), 1–8. Retrieved from https://sjmars.com/index.php/sjmars/article/view/12

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