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All Journal Mandalika Mathematics and Educations Journal Griya Journal of Mathematics Education and Application
Nuzla Af’idatur Robbaniyyah
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Education Mathematics

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Mapping of Flood Prone Areas in West Lombok Based on Analytic Hierarchy Process and Geographic Information System Nuzla Af’idatur Robbaniyyah; Syechah, Bulqis Nebulla; Naoval Husni; Marwan; Lailia Awalushaumi
Mandalika Mathematics and Educations Journal Vol 6 No 1 (2024): Edisi Juni
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v6i1.6542

Abstract

The development and management of flood-prone information systems is needed by many parties, especially the public. In this research, the Analytic Hierarchy Process (AHP) presents an approach to detecting flood-prone areas by combining it with a Geographic Information System (GIS). AHP analysis is used to determine the weight and value of each assessment criterion, and then the results are integrated into the GIS system to produce a flood forecast map. The results obtained show that mapping of flood-prone zones can be carried out rationally and consistently based on AHP by considering four criteria, namely land use, soil type, slope, and rainfall. The results of the analysis of the zoning map show that the areas with a high level of flood vulnerability are on the north and west sides. The area around the Lembar port has a high level of vulnerability. Eyat Mayang Village also has a high level of vulnerability. Locations with a high level of flood vulnerability, caused by flooding through rivers located not far from the sea estuary.
Analysis Of Solving Ordinary Differential Equations With A Comparison Of Adam-Bashforth Moulton And Milne-Simpson Methods Trias Kurnia; Neti Esta Wardaningsih; Ni Nengah Anggita Purwanti; Nuzla Af’idatur Robbaniyyah; Satriyantara, Rio
Griya Journal of Mathematics Education and Application Vol. 5 No. 4 (2025): Desember 2025
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v5i4.847

Abstract

Ordinary Differential Equations (ODEs) are mathematical models widely used in various fields of science and engineering to represent dynamic phenomena.. This study aims to compare the performance of two multi-step numerical methods, namely the Adams–Bashforth–Moulton (ABM) method and the Milne–Simpson (MS) method, in solving ordinary differential equations. The analysis was carried out by implementing both methods using the Python programming language and comparing their numerical results to the exact solution. Based on the simulation graphs, both methods produced results that closely matched the exact solution, with nearly overlapping curves throughout the time interval from zero to two. However, the absolute error analysis showed that the MS method generated smaller errors and a more stable error growth compared to the ABM method, especially at longer time steps. This indicates that although both methods are accurate, the Milne–Simpson method tends to be more stable over time. This study provides a comprehensive overview of the strengths of each method and can serve as a reference in selecting efficient and accurate numerical methods for solving ordinary differential equations.
Numerical Simulation of SIA Model in HIV/AIDS Using Euler and 4th OrderRunge-Kutta Method Dhity Rismawati; Livia Alda Rahmania; Naada Zahira; Nuzla Af’idatur Robbaniyyah; Satriyantara, Rio
Griya Journal of Mathematics Education and Application Vol. 5 No. 4 (2025): Desember 2025
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v5i4.921

Abstract

The HIV/AIDS epidemic remains a major public health issue, particularly in regions such as West Nusa Tenggara, Indonesia, where the number of reported cases continues to rise. To better understand and predict the spread of the disease, mathematical modeling provides a valuable analytical tool. This study employs the SIA (Susceptible-Infected-AIDS) compartmental model to describe the dynamics of HIV/AIDS transmission within the population. The model incorporates a latent phase, distinguishing it from simpler models and making it more suitable for diseases with long incubation periods such as HIV/AIDS. Two numerical methods, that is Euler and the 4th Order Runge–Kutta (RK4), are applied to solve the system of nonlinear differential equations derived from the model. Using official epidemiological data from 2023 in West Nusa Tenggara, the simulation tracks the evolution of the population across the three compartments over a 12-month period. The results indicate a consistent decline in the number of susceptible individuals and an increase in both infected and AIDS-diagnosed individuals. The basic reproduction number, , suggesting that the disease is endemic in the region. Stability analysis further confirms that the disease-free equilibrium is unstable, while the endemic equilibrium is locally asymptotically stable. These findings highlight the urgency of targeted interventions and demonstrate the importance of mathematical models in guiding public health strategies for disease control.
Co-Authors Dhity Rismawati Lailia Awalushaumi Livia Alda Rahmania Marwan Naada Zahira Naoval Husni Neti Esta Wardaningsih Ni Nengah Anggita Purwanti Rio Satriyantara Trias Kurnia