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Journal : EIGEN MATHEMATICS JOURNAL

 1 
Numerical Analysis of Mathematical Model for Diabetes Mellitus Disease by Using Adam-Bashfort Moulton Method Robbaniyyah, Nuzla Af’idatur; Salwa, Salwa; Maharani, Andika Ellena Saufika Hakim
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.245

Abstract

Diabetes mellitus is a metabolic disorder characterized by elevated blood glucose levels, known as hyperglycemia. The objective of this study is to develop a mathematical model of diabetes mellitus. The model will be analyzed in terms of its equilibrium points using the Adam-Bashforth Moulton numerical method. The numerical method that used is a multistep method. The predictor step employs the Runge-Kutta method, while the corrector step uses the Adam-Bashforth Moulton method. The mathematical model of diabetes mellitus is categorized into two classes: uncomplicated diabetes mellitus and complicated diabetes mellitus. The resulting model identifies two equilibrium points: the endemic equilibrium point (complicated) and the disease-free equilibrium point (uncomplicated). The eigenvalues of these equilibrium points are positive real numbers and negative real numbers. Therefore, the stability of the system is found to be unstable and asymptotically stable, indicating that the population of individuals with uncomplicated diabetes mellitus will continue to rise, whereas the population with complications will not increase significantly over time.
Solusi Numerik pada Persamaan Korteweg-De Vries Equation menggunakan Metode Beda Hingga Haizar, Maulana Rifky; Rizki, Miptahul; Robbaniyyah, Nuzla Af'idatur; Syechah, Bulqis Nebulla; Salwa, Salwa; Awalushaumi, Lailia
Eigen Mathematics Journal Vol 7 No 1 (2024): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i1.190

Abstract

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that has a key role in wave physics and many other disciplines. In this article, we develop numerical solutions of the KdV equation using the finite difference method with the Crank-Nicolson scheme. We explain the basic theory behind the KdV equation and the finite difference method, and outline the implementation of the Crank-Nicolson scheme in this context. We also give an overview of the space and time discretization and initial conditions used in the simulation. The results of these simulations are presented through graphical visualizations, which allow us to understand how the KdV solution evolves over time. Through analysis of the results, we explore the behavior of the solutions and perform comparisons with exact solutions in certain cases. Our conclusion summarizes our findings and discusses the advantages and limitations of the method used. We also provide suggestions for future research in this area.
Co-Authors Abd Kadir, Mujtahid Bin Abdurahim, Abdurahim Agus Kurnia Alfarikhi, Muhammad Solakhuddin Aminuyati Anwar Mustofa Arianti, Inggri Selpi Aribuabo, Anie Faye M. Asmarani, Evi Yuniartika Aulia, Sita Armi Ayu Liskinasih Choirunnisa, Fajarani Delia, Putri Elmustian Rahman Elmustian, Elmustian Endang Rahmawati, Endang Fathurrijal, Fathurrijal Febriansyah, Dwi Fiddien, Hasna Abidah Fitri Wulandari Fitriah Handayani Fitrya Ramadhani Gayatri, Marena Rahayu Haizar, Maulana Rifky Halimah, Hajar Nisa'ul Haq, Alfiyyah Dhiya'ul Harsyiah, Lisa Hermuttaqien, Bhakti Prima Findiga Hesti Aulia Ananda Hidayat, Malik Hidayatullah, Azka Farris I Gede Adhitya Wisnu Wardhana Irwansyah Irwansyah Jundana, Kholid Kusuma, Shendy Arya Lailia Awalushaumi Lailia Awalushaumi, Lailia Latri Aras, Latri Lestari, Sahin Two Liberte, Iman Aji Lilis Suryani Maharani, Andika Ellena Saufika Hakim Mardiah , Ainun Marwan Marwan Masyhuri Masyhuri Maulana Irfan, Maulana Misuki, Wahyu Ulyafandhie Muhammad Rijal Alfian Munawir, Ahmad Nghiem, Nguyen Dang Hoa Nurhabibah Nurhabibah Nurina Hidayah Onida Sinaga, Mawarta Pradana, Satriawan Purnamasari, Dara Putra, Lalu Riski Wirendra Putra, Sudarmadi Qudsi, Jihadil Qurratul Aini Ramadhan, Hikmal Maulana Ridia Juwita Dewi Rini Hartini Rinda Andayani Rio Satriyantara Riri Sundari Riskon Ginting Rizka Fadillah Rizki, Miptahul Robbaniyyah, Nuzla Af'idatur Robbaniyyah, Nuzla Af’idatur Salsabilla, Tarisya Zahwa Sari, Nena Puspita Satryantara, Rio Setiawati, Geta Siti Muawanah Soni Akhmad Nulhaqim Sri Sumarmi Suhadah Suhadah, Suhadah Sulaiman, Raden Muhamad Suprapmanto, Joko Syamsidar Gaffar Syamsul Bahri Syechah, Bulqis Nabula Tika, Dela Tri Maryono Rusadi Wardana, I Gede Adhitya Wisnu Widhi Sugianingsih, Ni Made yathroh, Isry Laila Yumni Awanis, Zata Yuni Sulistyowati, Yuni Yusron Saudi Zata Yumni Awanis Zikri, Lalu Muhammad Faiz Zulhan Widya Baskara