### Advanced Family of Newton-Cotes Formulas

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

H. Brass and K. Petras, Quadrature Theory: The Theory of Numerical Integration on a Compact Interval, No. 178, American Mathematical Soc. (2011).

C.O.E. Burg, Derivative-based closed Newton–Cotes numerical quadrature, Applied Mathematics and Computation 218 (2012), 7052 – 7065, DOI: 10.1016/j.amc.2011.12.060.

M. Chalpuri and J. Sucharitha, Open-type quadrature methods with equispaced nodes and a maximal polynomial degree of exactness, International Journal of Mathematics and Its Applications 55 (2017), 7.

S.C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill Science (2004).

P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, Courier Corporation (2007).

S.M. Hashemiparast, M.R. Eslahchi and M. Dehghan, Numerical integration using the derivatives, Applied Mathematics and Computation 180(1) (2006), 194 – 199, DOI: 10.1016/j.amc.2005.11.169.

T.M. Mills and S.J. Smith, A note on the Newton-Cotes integration formula, Journal of Approximation Theory 66(1) (1991), 98 – 105, DOI: 10.1016/0021-9045(91)90059-J.

W.W. Piegorsch, Durand’s rules for approximate integration, Historia Mathematica 16(4) (1989), 324 – 333, DOI: 10.1016/0315-0860(89)90079-7.

E. Sermutlu, Comparison of Newton–Cotes and Gaussian methods of quadrature, Applied Mathematics and Computation 171 (2005), 1048 – 1057, DOI: 10.1016/j.amc.2005.01.102.

DOI: http://dx.doi.org/10.26713%2Fjims.v10i3.773

eISSN 0975-5748; pISSN 0974-875X