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PENENTUAN RUMUS GAUSS KUADRATUR DENGAN MENGGUNAKAN PENDEKATAN INTERPOLASI HERMITE DAN POLINOMIAL ORTHOGONAL

KHOTIJAH, SITI (2012) PENENTUAN RUMUS GAUSS KUADRATUR DENGAN MENGGUNAKAN PENDEKATAN INTERPOLASI HERMITE DAN POLINOMIAL ORTHOGONAL. Other thesis, University of Muhammadiyah Malang.

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Abstract

Gauss quadrature is a numerical integration method that uses intervals of unequal length. It aims to get the error as small as possible. Gauss quadrature method to calculate the integral by taking the value of the function at some specific point that could represent a calculation of the balance of positive and negative errors. Approaches f (x) to the form of Hermite interpolation formula is expected to generate approaches E ≈ 0. Hermite interpolation formula product with w (x), and integrable on the interval [a,b] generates Hermite quadrature formula. Hermite quadrature formula can be correspondenced with Lagrange quadrature formula using the rules Orthogonal polynomials and some specific conditions such that both formulas are identical and form the Gauss quadrature formula. The base point and weight coefficients of Gauss quadrature can be obtained by using some properties Orthogonal polynomials. Use of the Gauss quadartur formula on ∫_a^b▒〖f(x)〗 dx convergent for ∀ x ϵ [a,b]. Function f (x) and its derivatives are limited to generating value E ≈ 0 and for f (x) the form of polynomials, the Gauss quadrature generated have E = 0. Several families of Orthogonal polynomials the Legendre polynomial, Lequerre, Hermite and Chebysev can be used to obtain specific types of Gauss quadrature formula that can be used to settle the boundary integral in accordance with a specified interval.

Item Type: Thesis (Other)
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Teacher Training and Education > Department of Mathematics Education (84202)
Depositing User: Gusti Vani Putri Cahya
Date Deposited: 03 Feb 2015 05:08
Last Modified: 03 Feb 2015 05:08
URI : http://eprints.umm.ac.id/id/eprint/15585

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