OPEN NEWTON - COTES QUADRATURE WITH MIDPOINT DERIVATIVE FOR INTEGRATION OF ALGEBRAIC FUNCTIONS

T. Ramachandran, R.Parimala

Abstract: Many methods are available for approximating the integral to the desired precision in Numerical integration. A new set of numerical integration formula of Open Newton-Cotes Quadrature with Midpoint Derivative type is suggested, which is the modified form of Open Newton-Cotes Quadrature. This new midpoint derivative based formula increase the two order of precision than the classical Open Newton-Cotes formula and also gives more accuracy than the existing formula. Further the error terms are obtained and compared with the existing methods. Finally, the effectiveness of the proposed algorithm is illustrated by means of a numerical example.

Keywords: Numerical Integration, Open Newton-Cotes formula, Midpoint Derivative, Numerical Examples.

DOI: https://doi.org/10.15623/ijret.2015.0410070