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Journal : M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika

Comparative Analysis of Numerical Integration Solutions Pias Method and Newton Cotes Method Using Python Programming Language Rahayu, Santi; Hindasyah, Achmad
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 8 No. 4 (2023): Mathline: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v8i4.492

Abstract

Irregular areas cannot be solved by ordinary calculus formulas, so it is necessary to use numerical methods such as the Quadrature and Newton-Cotes methods. This research compares numerical integration solutions using the Quadrature method (Rectangular and Trapezoidal) and the Newton-Cotes method (Trapezoidal, Simpson 1/3, Simpson 3/8, and Weddle) with the Python programming language. Manual calculation of the first case study on integrals where the smallest error from the numerical method to the analytical method is achieved by the rectangular method of 0,017. In the second case study of tabular data for manual calculations the author only uses the Simpson 3/8 method with an absolute error for an analytical area of 1.418,583 km2. Whereas in the Python application for the first case study the smallest error was achieved by the Simpson 1/3 and Simpson 3/8 methods with an error of 0, in the sense that these two methods are very accurate to the actual analysis results. In the second case study the smallest error was achieved by the Simpson 1/3 method of 1.039,365 km2. The difference between manual calculations and application results is due to decimal rounding, and the linspace(a,b,n+1) function in the numpy library.
Co-Authors Abdillah, Ahmad Fahmi Achmad Hindasyah, Achmad Ade Aulia Adelia Putri Ahmad Fa’idh Rifa’i Ahmad Rafli Oktavianto Almira Safana Anandika Yanuar Rahman, Hendi Anis Ilahi Putri Ardhie Firdaus Bahrein, Muhammad Birawa, Mahesa Budi Basuki Cakra Diningrat, Sobur Candra Himawan Devina Azzahra Putri Dini Juniarti Divan Dira Maulana Dwi Rizki Darmawan Dwi Santosa Fauziah, Shifa Firmansyah, Azrial Fredy Bagus Pranata Halawa, Hedwin Winata Hertanto Wahyu Subagio Hizbullah Sulthan Al Aziz Idham Nursyifa Hadiansyah Iis Istiqomah Ilham Fauzi Ilham Ramdhani Jidan Ramdani, Muhammad Jupron Jupron Khoirunnisa, Salsa Latifa Aini Susuma Latifa Suwari Fadilla M. Zidni Ilman Mahmudin Ais, Fiko Marcelino Mohammad Zen Rahfiludin Muhamad Fathuladim Muhamad Sopian Muhammad Ayub Yunus Muhammad Fadhillah Hafidh Muhammad Lintang Fahreza Muhammad Luthfi Muhammad Raffi Hermawan Muhammad Ramzi Muhammad Reynaldi Muhammad Shidqi Alwan Mujayanah, Arsil Muryati Muryati Nabila, Haula Hasna Nafa Ul Haq Azzahra Nazua Ditania Nurhaliza Zahra Ocha Alfiano Okta Irawati Pendianus Halawa, Gregorius Perani Rosyani Prasdio, Sendy Pratama, Sai Priatama, Yogi Rafli Arabiansyah Rahmat Hidayat Rahmat Ramdani Rasel Rubianto Raya Adinda Jayadi Ahmad Regina Maurita Rianto Putri Rivaldi Hidayatullah Rizki Maulana Febriansyah Rohimat Rusdiyanto Salsa Nisrina Putri Saputra, Riski Yoga Siswoyo Siswoyo Sutrisno Sutrisno Syach, Wahyu Addiyan Syakur, Roihan Aulia Tanjung, Yudistira Taufiq Muhaziz Teti Desyani Thohiriyah, Thohiriyah Tirta Adhi Samsara Tri Pudjadi Umar, Restu Aji Wina Febi Deaulya Putri