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All Journal Jurnal Review Pendidikan dan Pengajaran (JRPP) AKSIOMA : Jurnal Matematika dan Pendidikan Matematika
Muhammad Eka Suryana
UNJ
Economics, Econometrics & Finance Education Languange, Linguistic, Communication & Media Social Sciences Other

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KAJIAN METODE EKSTRAPOLASI RICHARDSON DAN AITKEN, SUATU METODE UNTUK MENGHITUNG INTEGRAL TERTENTU SECARA NUMERIK Mulyono Mulyono; Muhammad Eka Suryana; Pramudio Pramudio; Hazizi Hazizi; Bagus Sumargo Sumargo; Sri Sukatmi
Jurnal Review Pendidikan dan Pengajaran (JRPP) Vol. 6 No. 4 (2023): Volume 6 No 4 Tahun 2023
Publisher : LPPM Universitas Pahlawan Tuanku Tambusai

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31004/jrpp.v6i4.22639

Abstract

Penelitian ini bertujuan untuk menganalisa Metode Ekstrapolasi Richardson dan Metode Ekstrapolasi Aitken, yaitu metode untuk menghitung integral-integral tertentu secara numerik, khususnya untuk fungsi-fungsi yang sangat rumit, yang integralnya tidak bisa dihitung secara analitik. Faktor yang paling penting untuk dipertimbangkan dalam membandingkan metode-metode tersebut adalah akurasi dari penyelesaian numeriknya. Pada kajian ini digunakan software Microsoft Excel sebagai alat untuk membantu penghitungannya. Hasil dari kajian ini didapat bahwa Metode Ekstrapolasi Richardson lebih baik dari Metode Ekstrapolasi Aitken, karena akurasi hasil integral numerik dari metode Ekstrapolasi Richardson selalu lebih dibandingkan hasil integral numerik dari metode Ekstrapolasi Aitken.
Comparison of Gauss Quadrature and Newton–Cotes methods of order 10 in definite integral calculations Mulyono; Bagus Sumargo; Muhammad Eka Suryana; Ratna Widyati
AKSIOMA: Jurnal Matematika dan Pendidikan Matematika Vol. 17 No. 1 (2026): AKSIOMA: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas PGRI Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26877/jdxqqz70

Abstract

This study aims to evaluate and compare the accuracy of the Gauss Quadrature Method and the 10th Order Newton–Cotes Method based on numerical error in computing definite integrals, especially for complex functions that are difficult to solve analytically. The Gauss Quadrature Method studied includes the use of 2-point, 3-point, 4-point, 5-point, and 6-point rules, where the term points refers to the number of nodes used in the integration process. In contrast, the 10th-order Newton–Cotes Method is used for comparison, based on a high-degree interpolation polynomial at equidistant points. The comparison of the two methods is based on the accuracy of the numerical results as the main criterion. In this study, Microsoft Excel is used as a tool for numerical calculations. The results show that the Gauss Quadrature Method with 6 points provides numerical integral results with the highest level of accuracy compared to the Gauss Quadrature Method with fewer points, but generally produces larger errors than the 10th Order Newton–Cotes Method. These results indicate that, for the cases considered in this study, the 10th-order Newton–Cotes method is more efficient and accurate for calculating definite integrals.
Co-Authors Bagus Sumargo Bagus Sumargo Sumargo Hazizi Hazizi Mulyono Mulyono Mulyono Pramudio Pramudio Ratna Widyati Sukatmi, Sri