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Journal : Journal of Mathematics UNP

Penentuan Akar Persamaan Non Linier Menggunakan Metode Iterasi Tanpa Menghitung Turunan yang Lebih Tinggi Olpelda, Danisa Alzura; Subhan, Muhammad
Journal of Mathematics UNP Vol 9, No 3 (2024): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v9i3.16230

Abstract

The iteration method without calculating higher derivatives is one of the numerical methods which is included in the group of open methods. This iteration method is derived based on the third truncated Thiele’s continuous fraction. To avoid calculating higher derivatives, an approximation of the second and third derivatives is used in determining the roots. This research aims to determine the roots of non-linear equations using the iteration method without calculating higher derivatives. This type of research is basic research. Based on the discussion results, it was found that the iteration method without calculating higher derivatives uses two-step in determining the root. The convergence analysis shows that the iteration method without calculating higher derivatives has a convergence order of four. The algorithm of the iteration method without calculating higher derivatives is shown in the form of a flowchart.Keywords: Non-linear equation, Thiele’s continued fraction, Viscovatov algorithm, iterative method, order of convergence
Implementasi Fuzzy Time Series Logika Singh Untuk peramalan Nilai Ekspor Nilam di Indonesia Putri, Rahmadita Amalia; Subhan, Muhammad
Journal of Mathematics UNP Vol 10, No 1 (2025): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v10i1.17047

Abstract

Patchouli is used as one of the mixtures of cosmetic products, food industry, paint making, aromatherapy, and various other industrial needs and is needed by various types of industries in various countries. Due to the high world demand for patchouli, a prediction is made to anticipate uncertainty so that an estimate is obtained that is close to the actual situation. The method that can be used is the Singh logic fuzzy time series method. This research is an applied research, where the data taken is the data on the value of patchouli exports in Indonesia in the period January 2020 to July 2024. The results of forecasting the value of patchouli export data in Indonesia with this method are then measured for accuracy using MAPE. From the Singh logic fuzzy time series forecasting method, the MAPE obtained was 7,215%. Based on the MAPE, forecasting export value in Indonesia with Singh's fuzzy time series logic has a very good level of accuracy. For the following period, the export value of patchouli is projected to be US$ 29,638,657.15 for August 2024, US$ 28.212.795,11 for September 2024, and US$ 28.277.533,23 for October 2024. The Predicted value is categorized qith a very high export value of patchouli.
PENENTUAN AKAR PERSAMAAN POLINOMIAL KUARTIK DENGAN PENDEKATAN PERLUASAN METODE CARDANO Susanti, Yepsi; Subhan, Muhammad
Journal of Mathematics UNP Vol 9, No 4 (2024): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v9i4.16888

Abstract

Persamaan Polinomial kuartik adalah persamaan polinomial yang memiliki pangkat tertinggi yaitu empat. Salah satu permasalahan persamaan polinomial kuartik adalah mencari solusi akar dari persamaan polinomial kuartik. Tujuan dari penelitian ini adalah membentuk formula dan menyusun langkah-langkah dari Perluasan Metode Cardano. Metode yang digunakan dalam penelitian ini adalah studi literatur. Berdasarkan hasil penelitian diperoleh bahwa bentuk formula Perluasan Metode Cardano memiliki rumus kuadrat yang menghasilkan empat nilai kemudian disubstitusikan ke rumus akar sehingga menghasilkan empat akar persamaan polinomial kuartik yaitu yang memiliki akar rill dan kembar pada diskriminan sama dengan nol, akar rill dan berlainan pada diskriminan besar dari nol, serta akar kompleks pada diskriminan kecil dari nol. Selanjutnya diperoleh langkah-langkah dari Perluasan Metode Cardano yaitu tentukan nilai k,l,m,n, tentukan nilai p,q,r,z,D, dalam z besar dari nol dan kecil sama dengan empat berdasarkan persamaan kubik resolven, dan masukkan nilai z dalam formula Perluasan Metode Cardano yang didapat.
Metode Iteratif Bebas Turunan Tinggi Untuk Persamaan Non Linear Fhadilah, Syafirna; Subhan, Muhammad
Journal of Mathematics UNP Vol 9, No 3 (2024): Journal Of Mathematics UNP
Publisher : UNIVERSITAS NEGERI PADANG

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/unpjomath.v9i3.16669

Abstract

To find the roots of non-linear equations, numerical methods such as Newton-Raphson and Secant are often used when analytical approaches are difficult to apply. However, these methods are relatively slow due to their low convergence order. Iterative methods with higher convergence orders can speed up the process, but they often involve more complicated derivatives. To overcome this, a high derivative-free iterative method was developed using the predictor and corrector approach. This research aims to develop the method, analyze its convergence order, and develop its algorithm. This research is a theoreticalresearch by reviewing the theories related to the problem at hand. The results show that the new method has a convergence order of six, is faster than the Newton-Raphson and Secant methods in solving non-linear equations, and only involves the first derivative. 
Co-Authors Abdillah Halim Abdul Gafur Abdul Rauf Adi Pratama, Adi Afril Lestari, Windi Agrippina Wiraningtyas, Agrippina Agustina Mutia Ahmad Bashawir Abdul Ghani Aisa, Aufia Aisyah, Ovina Akbar, Faris Akhyar, Mushtofainal Alfaini, Ainul Yaqin Alfian, Muhammad Faizal Ambok Pangiuk Aminah, Ummu Amril Amril Ananda, Aldila Andang, Andang Andika Andika Anggraheni, Palupi Anis Rachma Utary Anita, Efni Anwar, Fahrizal Aprillia, Pita Ariandi_saputra Ariansyah , Ariansyah Arif Munandar Arisman Arisman Armiati Arsa Arsa Astuti, Amanda Febri Aswin , Fajar Auliana, Rini Aurelsosa, Langlang Soeltanul Aulia Azhara, Putri Indah Azmiati, Vivilia Bakhtiar, Muh. Irham Buhari Buhari Damayanti, Wa Ode Astika Damiri, Teuku Farhan Darniyanti, Yulia Delmayani, Delmayani Delvianti, Sintia Dewi Setyaningsih Dian Permata Sari Diaz, Yohana Grezia Djalipa, Dedy Dwi Ramadina, Novia Arista Dwi Supriyanto, Muhammad Sofyan efindel, Sintia Delvianti eka rahmawati Elistia Liza Namigo, Elistia Emilda Kuspraningrum Erwin Saputra Siregar Fadhillah, Hafiz Fahrudin Fahrudin Faidin Faidin Fajrun, Fajrun Farhan, Muhammad Miftah Fatharini, Anjani Tri Fendy Eko Wahyudi, Fendy Eko Fhadilah, Syafirna Firdaus, Dadan Ghazali, M. Gunawan, Dede Reza Hadi, Dedi Abdul Hamzah, Hasyrul Hardi Warsono Hasdiansah, Hasdiansah Hawahera, Citra Hermini Susiatiningsih Hidayat, Ahmad Fadel Syakir Hidayati, Zuhriyyah Hudaya, Maula Husin, Nikson Husti , Iyas I Ketut Widnyana I Made Wahyu Wijaya Ifandi Ifandi Ika Riswanti Putranti Ikhsan Abdullah Imanuddin, Akbar Indah Riezky Pratiwi Indrawan, Boby Iqbal, Adi Irma Rubianti Jalalul Akbar, Said Jannah, Ummi Nur Jumni Nelli Karomah, Asror Kautsar Eka Wardhana Kibtiyah, Mariatul Kunnuzi , Kunnuzi Kurnia Putri, Fera Kusumawikan, James William Lasmijiani, Lasmijiani Lestari, Evi Endha Mahmudi, Moh Rosyid Mansurotin, Titin Marniati Kadir Marten Hanura, Marten Masdani, Masdani Masitah Masitah MAULANA, RIZA Maulani Meutia Rani Mayangsari, Ita Medyan Riza Meidina, Mutiara Alda Miftah, AA Minora Longgom Nasution Mubarak, M. Ali MUHAMMAD AGIL Muhammad Iqbal Mundzir, Ali Muslim Afandi Nasrullah, Aditya Nelli , Jumni Ni Putu Cempaka Dharmadewi Atmaja Nisa, Hairun Nisa Nofriza, Eri Novi Sylvia Nura, Faris An Nurwijayanti Olahairullah, Olahairullah Olpelda, Danisa Alzura Paganizza, Valeria Pane, Astriana Sitorus Prakasa, Bayu Pratama, Virgiawan Yoga Pristiansyah, Pristiansyah Putri, Rahmadita Amalia Putriyani, Febby Putu Eka Pasmidi Ariati Rabiatul Adawiah Rahayu Retnowulan, Sri Rahmadhani, Raudha Rahmah, Avivah Rahmawati, Rina Dian Ratnawati Ratnawati Risma Deviyanti, Dwi Rizal, Moh Syaiful Ronal Rifandi Rozanna Dewi Rusita Dewi, Sintya Trisna Saddam Al Aziz Safitri, Auliya Nur Salianto Salianto, Salianto Salmitha, Lely Sandia, Eci`` Savitri, Viora Roza setiyaningsih, dewi Shodiqin, Ghufron Shofiyani, Amrini Sissah Sissah Siswono, Hendrik Sri Rejeki Sri Wulandari Sucipto Sucipto Sukamto, Ika Sumiyarsi Sukanto , Sukanto Susanti, Yepsi Susanto, Willy Suswati, Lis Suzen, Zaldy Sirwansyah Sya'roni, Muhammad Syafruddin, A. Ummu Fauziyyah Syirad Ramadhan, Yusuf Sylvia Utami Tunjung Pratiwi Taswin, Taswin Taufiq, La Ode Muh. Trisnawati, Ice Umami, Fahmi Najah Viniolita, Thala Warahma, Izrha Yatmikasari, Ika Yemimaria, Yemimaria Yonesa, Salsabila Yuliyanto Yuliyanto Yulyanti Harisman Zainal Abidin, Moh Ali Zaldy Kurniawan Zayyan, Muhammad Zada Zuliyan, Muhammad Arief