A Proposed Numerical Integration Method Using Polynomial Interpolation
Kwasi A. Darkwah *
Department of Statistics, University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical Sciences, Ghana.
Ezekiel N. N. Nortey
Department of Statistics, University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical Sciences, Ghana.
Charles Anani Lotsi
Department of Statistics, University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical Sciences, Ghana.
*Author to whom correspondence should be addressed.
Abstract
The main aim of this paper is to propose a numerical integration method using polynomial interpolation that provides improved estimates as compared to the Newton-Cotes methods of integration. The method is an extension of trapezoidal rule where the Lagrange interpolation is employed when fitting polynomials after segmentation. We proved that the proposed numerical integration method using polynomial interpolation provided an improved formula for numerical integration. The proposed method using polynomial interpolation gave better estimates as compared to some Newton-Cotes methods of integration.
Keywords: Numerical integration, polynomial interpolation, Newton-Cotes methods, relative error.