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PERBANDINGAN KETELITIAN APROKSIMASI INTEGRAL ANTARA METODE EKSTRAPOLASI RICHARDSON DAN METODE EKSTRAPOLASI AITKEN DENGAN PROGRAM MICROSOFT EXCEL

AGUSTINA, WINDA (2012) PERBANDINGAN KETELITIAN APROKSIMASI INTEGRAL ANTARA METODE EKSTRAPOLASI RICHARDSON DAN METODE EKSTRAPOLASI AITKEN DENGAN PROGRAM MICROSOFT EXCEL. Other thesis, University of Muhammadiyah Malang.

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Abstract

Integral is one of the basic subjects in addition to the derivatives. It is application in daily activities such as sains and engineering. But not all can be solved analytically. Occasionally there is a complicated function for integrable such as functions are presented in tabular form. Extrapolation is a numerical methods that could be used to solve the integral problems to the approach of Richardson extrapolation and Aitken extrapolation. The study aimed at : (1). Investigating integral approximation procedures of Richardson method, (2). Investigating integral approximation procedures of Aitken method, (3). Investigating the integral approximation accuracy comparison between Richardson and Aitken methods with Microsoft Excel program. Integral functions proceeded for approximation are tabulated and complex continous functions by using SimpsonÂ’s Rule 1/3. These functions have limit and width within interval (h)<1. Richardson extrapolation method is the integral approximate method based on the rule that is standard with wide distances between the points h and recalculate the distance between point width h / 2 with known the order of error to get a better integration. Meanwhile, Aitken extrapolation method calculate the distance between the point width h/2 and h/4 with unknown the order of error. The finding showed that the integral approximately by Aitken extrapolation methods has an average relative error less0,022416558 %than Richardson extrapolation in the amount of 0,223792134 %. In conclusion, Aitken extrapolation method showed better approximation accuracy than the Richardson extrapolation.

Item Type: Thesis (Other)
Subjects: L Education > L Education (General)
Divisions: Faculty of Teacher Training and Education > Department of Mathematics Education (84202)
Depositing User: Gusti Vani Putri Cahya
Date Deposited: 02 Feb 2015 04:14
Last Modified: 02 Feb 2015 04:14
URI : http://eprints.umm.ac.id/id/eprint/15505

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