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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 Ainul Yaqin alfi husni, alfi Alfiana Alfiana Alfroni, Yohana Fransiska Ali Maulida, Ali Amelia, Sifa Andani, Hamdan Anindya, Regita Ariansyah, Arif Arijulmanan, Arijulmanan Arisandi, Oriza Asmawati Asmawati Asrofiani, Dwi Azhari, Lukman Batlolona, John Rafafy Bimasri, Jhon Bimasri, John Budiarti, Laras Ayu Putri Danarti Karsono Desella Inna Rahmatina, Desella Inna Diana Dewi Wahyuningsih Donita, Salwa Audriana DWI NINGSIH SUSILOWATI Dwicahya , Nadya Elfira Safitri Elmarma, Fazlur Rahman Erison, Yendra Erni Widarti Etty Safriyani Faiz Muqorrir Kaaffah Farida Farida Fatkhurohman, Irfan Fauzi Ahmad Muda Fitri Amalia Grusche, Sascha Hadi, Izzul Havidz Cahya Pratama Hermanto Holidi Holidi Indera, Edi Indrawan, Mohamad Gita Irma Suryani Iskandar Iskandar 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 Mulyadi Mulyadi Muspida, Muspida Nazvira, Mutia Nirmalasari, Cyntia Nirmalasari, Cyntia Pamungkas, Muh. Rizal F. Pamungkas, Muhammad Rizal Fernandita Panusunan, Panusunan Permatasari, Lintang Ayu Pratama, Rahmadhani Prayitno, M. Hadi Puji Hapsari, Elsa PUJI LESTARI Purwasih, Hari Dewi Puspita, Alisa Zulia Putri, Rahmadhani Yulmi Putri, Revandra Thalitha Kumala Rahendra Maya, Rahendra Rahman Rahman Rakhadani, Ihrom Ramadhani, Argia Putri Rasid, Husni Muhammad Rinda Kirana Riry Sriningsih Rizal Fernandita Pamungkas, Muhammad Rohmah, Eva Nur Laily Roni, Roni Rudiansyah Rundi, Allesandro U.B. Rundi, Allesandro Umbu Balla Saifuddin Saifuddin Sandi, Elisa Harlia Santi, Neng Sentot Kusairi Septiana, Ambar Setiawan, Hamdan Setyawati, Nisrina Yulia Setyo Nugroho, Imam 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 Sutopo Sutopo Syahputra, Ridwan Angga Takaria, Johannis Takaria, Johannis Tri Wulandari, Fera 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