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All Journal M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jurnal Abdimas Ilmiah Citra Bakti (JAICB) Jambura Journal of Biomathematics (JJBM) Jurnal Media Informatika Jurnal Pijar MIPA
Hurit, Roberta Uron
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Agriculture, Biological Sciences & Forestry Arts Humanities Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Education Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Mathematics Physics Social Sciences

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The Euler, Heun, and Fourth Order Runge-Kutta Solutions to SEIR Model for the Spread of Meningitis Disease Hurit, Roberta Uron; Sudi Mungkasi
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol 6 No 2 (2021): Mathline
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v6i2.176

Abstract

Penelitian ini bertujuan untuk menyelesaikan model SEIR penyebaran penyakit meningitis menggunakan metode Euler, metode Heun dan metode Runge-Kutta orde empat, dimana model persamaannya berupa persamaan diferensial nonlinear. Metode penelitian yang digunakan adalah pemrograman komputer dan simulasi. Dari simulasi, ketiga metode tersebut menghasilkan penyelesaian dengan perilaku yang mirip, yaitu semua gambar grafik pada setiap simulasi mempunyai bentuk pola yang sama. Hal ini memberikan kepercayaan pada kebenaran hasil simulasi dalam makalah ini. Secara teori, metode Runge-Kutta orde empat memiliki ketelitian yang lebih tinggi dibandingkan dengan metode Euler dan metode Heun. Kata Kunci: penyebaran penyakit meningitis, model SEIR, metode Euler, metode Heun, metode Runge-Kutta orde empat.
Comparison of Optimal Control Effect from Fungicides and Pseudomonas Fluorescens on Downy Mildew in Corn Ludji, Dian Grace; Hurit, Roberta Uron; Manek, Siprianus Septian; Ndii, Meksianis Z
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.23153

Abstract

Downy mildew is a disease that continues to infect corn crops in Timor Tengah Utara regency, reducing the amount of crop production and making corn farmers suffer losses. Farmers continue to look for ways to control downy mildew. Two treatments are commonly used by farmers, namely spraying Fungicides and Pseudomonas Fluorescens simultaneously in one unit of time, but have not resulted in optimal production. Therefore, this research is important to get a more optimal way to control find downy mildew. In this paper, we determine the optimal model of downy mildew control in corn plants by comparing the use of Fungicides and Pseudomonas Fluorescens. This research begins by forming a dynamic mathematical model consisting of six populations, namely four corn populations (Sh, F , P , Ih) and two populations of infecting fungi (Sv , Iv ). Then they obtained the basic reproduction number (R0) and two equilibrium points, namely the disease-free equilibrium and the disease-endemic equilibrium which has asymptotic stability. Numerical simulation results based on optimal control analysis with the minimum Pontryagin principle show that using fungicides can reduce the number of plants infected with downy mildew. Therefore, control by using fungicides is necessary and recommended increasing the number of downy mildew infected plants.
The Euler, Heun, and Fourth Order Runge-Kutta Solutions to SEIR Model for the Spread of Meningitis Disease: Penyelesaian Euler, Heun, dan Runge-Kutta Orde Empat atas Model SEIR pada Penyebaran Penyakit Meningitis Hurit, Roberta Uron; Sudi Mungkasi
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 6 No. 2 (2021): Mathline
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v6i2.176

Abstract

Penelitian ini bertujuan untuk menyelesaikan model SEIR penyebaran penyakit meningitis menggunakan metode Euler, metode Heun dan metode Runge-Kutta orde empat, dimana model persamaannya berupa persamaan diferensial nonlinear. Metode penelitian yang digunakan adalah pemrograman komputer dan simulasi. Dari simulasi, ketiga metode tersebut menghasilkan penyelesaian dengan perilaku yang mirip, yaitu semua gambar grafik pada setiap simulasi mempunyai bentuk pola yang sama. Hal ini memberikan kepercayaan pada kebenaran hasil simulasi dalam makalah ini. Secara teori, metode Runge-Kutta orde empat memiliki ketelitian yang lebih tinggi dibandingkan dengan metode Euler dan metode Heun. Kata Kunci: penyebaran penyakit meningitis, model SEIR, metode Euler, metode Heun, metode Runge-Kutta orde empat.
MATH IS FUN: PEMBUATAN ALAT PERAGA MATEMATIKA UNTUK MENINGKATKAN PEMAHAMAN KONSEP SISWA SDK SANTA CARMEN SALLES Kumanireng, Ince; Hurit, Roberta Uron
Jurnal Abdimas Ilmiah Citra Bakti Vol. 6 No. 2 (2025)
Publisher : STKIP Citra Bakti

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38048/jailcb.v6i2.5139

Abstract

Permasalahan mitra dalam kegiatan ini adalah rendahnya pemahaman konsep matematika siswa, kurangnya motivasi belajar, serta terbatasnya penggunaan alat peraga yang kontekstual dan menyenangkan di SDK Santa Carmen Salles. Tujuan dari kegiatan pengabdian ini adalah untuk meningkatkan pemahaman konsep dan ketertarikan siswa terhadap pelajaran matematika melalui pelatihan dan praktik pembuatan alat peraga edukatif berbasis pendekatan "Math is Fun". Mitra kegiatan terdiri dari guru kelas dan 30 siswa kelas V SDK Santa Carmen Salles. Metode pelaksanaan meliputi pendekatan partisipatif dengan tahapan persiapan, pelaksanaan, dan evaluasi. Teknik yang digunakan adalah pelatihan, demonstrasi, praktik langsung, observasi, wawancara, dan dokumentasi. Hasil kegiatan menunjukkan bahwa siswa lebih aktif, antusias, dan menunjukkan peningkatan pemahaman konsep pecahan, sudut, dan sistem nilai tempat. Guru juga memperoleh pengetahuan baru dalam menciptakan media belajar yang sederhana namun efektif. Kesimpulannya, kegiatan pengabdian ini mampu meningkatkan pemahaman konsep matematika sekaligus menumbuhkan motivasi dan keterlibatan aktif siswa dalam proses pembelajaran melalui media konkret yang kontekstual dan menyenangkan.
Analisis Model Sleiqr Pada Penyebaran Penyakit Covid-19 Nuhan, Agnes Marselina; Hurit, Roberta Uron; Muaraya, Irwanius P.
Jurnal Media Informatika Vol. 6 No. 4 (2025): Jurnal Media Informatika
Publisher : Lembaga Dongan Dosen

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55338/jumin.v6i4.6663

Abstract

The objective of this research is to address the SLEIQR mathematical model associated with the transmission of COVID-19 by employing the Euler and Heun numerical techniques. The SLEIQR model is structured as a set of nonlinear differential equations that categorizes the population into six compartments: Susceptible (S), Closed (L), Exposed (E), Infected (I), Quarantined (Q), and Recovered (R). The approach adopted in this research is a literature review combined with a numerical method, wherein simulations are conducted using MATLAB under two distinct scenarios. The findings from the simulations suggest that the application of closure and quarantine measures can diminish the rate of increase in the number of infected individuals. Both methods yield comparable results in terms of solution behavior; however, the Heun method demonstrates a higher degree of accuracy. Therefore, the Heun method is recommended for use in simulating intricate infectious disease transmission models such as COVID-19.
Solution of the Sir Epidemic Model for the Spread of Tuberculosis Using the Fourth Order Runge-Kutta and Milne Method Hurit, Roberta Uron; Lapeng, Veronica; Muaraya, Irwanius P.
Jurnal Pijar Mipa Vol. 20 No. 6 (2025)
Publisher : Department of Mathematics and Science Education, Faculty of Teacher Training and Education, University of Mataram. Jurnal Pijar MIPA colaborates with Perkumpulan Pendidik IPA Indonesia Wilayah Nusa Tenggara Barat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jpm.v20i6.10083

Abstract

Tuberculosis (TB) is an infectious disease of the human respiratory tract caused by the bacterium Mycobacterium tuberculosis (Mtb). The bacteria that cause TB are a type of bacillus bacteria that are very strong, so it takes a long time to treat this TB disease. This research is a literature study examining the mathematical model of SIR in TB disease. This research involves several stages, including the numerical integration of the SIR model, converting the resulting model into a computer programming language, performing numerical simulations, and observing solution graphs. This study aims to solve the SIR model of tuberculosis transmission using the fourth-order Runge-Kutta method and the Milne method. The resulting SIR model is a nonlinear differential equation model. The object of research in this study is the SIR Mathematical Model. The procedure for creating the SIR mathematical model consists of seven steps: case identification, establishing assumptions, creating the mathematical model, model analysis, model interpretation, model validation, and using the model. The research method employed is a literature study approach with a numerical component. Simulations were carried out twice for each method. The results of the numerical simulation in the MATLAB program show that both methods produce solutions with similar behaviour. However, in theory, the Milne method has a higher level of accuracy than the fourth-order Runge-Kutta method. The graph also shows that a population/individual suffering from tuberculosis will recover over time, assuming they undergo treatment or adopt a healthy lifestyle. The infection population will experience a decline towards an equilibrium point as time passes.
Co-Authors Dian Grace Ludji Kumanireng, Ince Lapeng, Veronica Muaraya, Irwanius P. Ndii, Meksianis Z Nuhan, Agnes Marselina Siprianus Septian Manek