TY  - JOUR
T1  - A New Approach for the Derivation of Higher-Order Newton-Cotes Closed Integration Formulae
AU - , J.O. Fatokun AU - , H.K. Oduwole 
JO  - Journal of Engineering and Applied Sciences
VL  - 2
IS  - 9
SP  - 1460
EP  - 1464
PY  - 2007
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2007.1460.1464
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2007.1460.1464
KW  - Newton-cotes
KW  -integration formulae
KW  -Lagrange’s interpolation
KW  -polynomial functions
KW  -finite differences
KW  -closed formulae
AB  - This study concerns the derivation of higher order Newton-cotes closed integration using Lagrange’s interpolation polynomial functions. In literature, the conventional way of deriving these integration formulae is by making the x<SUB>i </SUB>equally spaced, so that there are only n+1 parameters a<SUB>i</SUB> to choose. The coefficients are then fixed either by using finite difference results or by considering it as a general formula with various coefficients which must be fixed. William presents coefficients for orders p = 1, 2,...8 . In this research, an extension of this was carried out for orders p = 9, 10, 11. Ralston gave a detailed mathematical treatment of the error analysis for the known Newton Cotes formulae of orders p=1,2,…,8. These manipulations are extremely cumbersome since it involves n+1 conditions and hence solving a large system of algebraic equations. This led to the new approach of using the Lagrange’s interpolation functions to derive the Newton Cotes Closed formulae of orders p = 1,2,…,11. A generalized formula was developed for order p=k. These methods were applied to some integrals such as exponential function and trigonometric functions. The numerical results show that higher order methods are needed for equally spaced intervals to increase the accuracy of the general Newton-cotes closed formulae.
ER  -