OPTIMAL NUMERICAL INTEGRATION BY GAUSS-LEGENDRE QUADRATURES

Shaini, Bilall (2019) OPTIMAL NUMERICAL INTEGRATION BY GAUSS-LEGENDRE QUADRATURES. Journal of Natural Sciences and Mathematics of UT, 4 (7-8). pp. 229-237. ISSN 2671-3039

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Abstract

We will consider the problem of numerical quadrature of a definite integral in cases where the integrand is not explicitly known, ie it is given in the form of tabular data or as a points , or when the function can not be integrated with elementary algebraic transformations. We will briefly describe the Newton-Cotes integration formulas and their corresponding error estimates. Furthermore, we will provide a general form of Gauss quadrature formulas in which weight functions are orthogonal polynomials. In this paper, we will consider numerically integrating Gauss-Legedre's formulas, that is, when the weight function is in the Legendre polynomial class. We will show two ways to generate Legendre polynomials and some of them will be graphically presented. Using the Mathematica program package through specific examples for numerical computation of the integral, when comparing the results with classical Newton-Cotes formulas, it turns out that Gauss-Legedre's quadratures give apparent better results in evaluating the error of the method, as well as with a reduced number of steps in executing the algorithm to achieve the required accuracy.

Item Type:	Article
Subjects:	Q Science > Q Science (General)
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	22 Feb 2020 18:41
Last Modified:	22 Feb 2020 18:41
URI:	http://eprints.unite.edu.mk/id/eprint/460

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