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Journal : KADIKMA

MODIFIKASI METODE HANSEN-PATRICK DENGAN ORDE KONVERGENSI OPTIMAL UNTUK MENYELESAIKAN PERSAMAAN NONLINIER wartono, wartono
Kadikma Vol 13 No 2 (2022): Agustus 2022
Publisher : Department of Mathematics Education , University of Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/kdma.v13i2.32202

Abstract

The Hansen-Patrick method is a third-order iterative method used to solve nonlinear equation. The method requires three evaluation of functions and has an efficiency index 31/3 » 1,4224. This study discusses a modification of the Hansen-Patrick method using the second order Taylor series. The second derivative is reduced using hyperbolic function with one parameter h. The aim of modification is to improve the convergence order of the Hansen-Patrick’s method. Based on the convergence analysis, the method has a fourth-order of convergence and envolve three evaluation of functions. So, its efficiency index is 41/3 » 1,5874. Numerical simulation is given to illustrate performance of the iterative method using six real functions. The performance of the iterative method include : a computational order of convergence, the number of iteration, evaluation of function, absolute error, and value of function, will be compared with Newton’s method, Halley’s method, Newton-Steffensen’s method, and Hansen-Patrick method. The numerical simulation shows that the performance of the method better than others
Co-Authors Agus Sarifudin, Agus Agustina, Annisa alfi husni, alfi Alfiana Alfiana Alfroni, Yohana Fransiska Ali Maulida, Ali Amelia, Sifa Andani, Hamdan Anindya, Regita Ariansyah, Arif Arijulmanan, Arijulmanan Arisandi, Oriza Asrofiani, Dwi Azhari, Lukman Batlolona, John Rafafy Bimasri, Jhon Bimasri, John Danarti Karsono Donita, Salwa Audriana DWI NINGSIH SUSILOWATI Dwicahya , Nadya Elfira Safitri Elmarma, Fazlur Rahman Erison, Yendra Erni Widarti Etty Safriyani Faiz Muqorrir Kaaffah Farida Farida Fauzi Ahmad Muda Fitri Amalia Grusche, Sascha Hadi, Izzul Hermanto Holidi Holidi Indera, Edi Indrawan, Mohamad Gita Irma Suryani Jayanti, Y. M. Jayanti, Y. M. Khofid, Adi Nur Komalasari, Nyai Lestari, Ega Lia Yuliati, Lia Lifianthi, Lifianthi Mahapoonyanont, Natcha Malik, Akmal Moh. Erkamim Mohammad Soleh Muhafzan Muhafzan Muhammad Arif Muhammad Hidayat Ginanjar, Muhammad Hidayat Muhammad Nur Hudha Muspida, Muspida Nazvira, Mutia Nirmalasari, Cyntia Nirmalasari, Cyntia Pamungkas, Muh. Rizal F. Pamungkas, Muhammad Rizal Fernandita Panusunan, Panusunan Permatasari, Lintang Ayu Prayitno, M. Hadi PUJI LESTARI Puji Susanti, Rini Purwasih, Hari Dewi Puspita, Alisa Zulia Putri, Rahmadhani Yulmi Rahendra Maya, Rahendra Rahman Rahman Rakhadani, Ihrom Ramadhani, Argia Putri Rasid, Husni Muhammad Rinda Kirana Riry Sriningsih Rohmah, Eva Nur Laily Roni, Roni Rudiansyah Rudiansyah, Rudiansyah Rundi, Allesandro U.B. Rundi, Allesandro Umbu Balla Saifuddin Saifuddin Sandi, Elisa Harlia Santi, Neng Setiawan, Hamdan Setyawati, Nisrina Yulia Sholihuddin, M Nur Siti Fatimah Azzahra SOLAHUDIN SOLAHUDIN, SOLAHUDIN Sulasiwi, Intan Febry Sumarjono Sumarjono Sumini Sumini, Sumini Sumpena, Sumpena Supriyono Koes Handayanto Supriyono Supriyono Suryani Suryani Susanti, Rini Puji Syahputra, Ridwan Angga Takaria, Johannis Takaria, Johannis Trianto, Joko Ujang Andi Yusuf, Ujang Andi Unang Wahidin, Unang Wati, Dewi Gislia Wati, Vera Yadi Suryadi Yasyakur, Moch Yuanita FD Sidabutar Yuslenita Muda Zakaria, Aceng