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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Research Journal of Life Science Telematika Edumatsains MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Indonesian Journal of Mathematics and Applications
Habibah, Ummu
Universitas Brawijaya
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Education Mathematics Medicine & Pharmacology Physics Other

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Comparison Study between Shooting and Finite Difference Methods for Solving Linear Boundary Value Problem with Dirichlet, Neumann, and Robin Boundary Conditions Ardiana, Dita; Rachman, Alifira Meliana; Nurkarimah, Dwi; Habibah, Ummu
Indonesian Journal of Mathematics and Applications Vol. 3 No. 1 (2025): Indonesian Journal of Mathematics and Applications (IJMA)
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2025.003.01.2

Abstract

This study conducts a comparative analysis of the Shooting and Finite Difference methods for solving boundary value problems (BVPs) in ordinary differential equations (ODEs). The findings indicate that the Shooting method offers superior accuracy, particularly for smaller step sizes, whereas the Finite Difference method is more straightforward to implement and exhibits greater computational efficiency. The results further demonstrate that the Shooting method is particularly highly appropriate for problems with Dirichlet boundary conditions, as it achieves the lowest mean absolute error (MAE) across various step sizes. Conversely, the Finite Difference method attains higher computational efficiency for the same problem type but performs less advantageously in cases involving other boundary conditions. In contrast, the Shooting method demonstrates greater efficiency in solving problems with Neumann and Robin boundary conditions. The selection of an appropriate numerical method depends on the specific characteristics of the problem, necessitating a balance between accuracy and computational cost. This study provides a comprehensive evaluation of these numerical approaches to support the selection of the most suitable method for efficiently and accurately solving BVPs.
Dynamical Analysis and Optimal Control of Breast Cancer Patient Model Muniroh, Kunnisai; Habibah, Ummu; Kusumawinahyu, Wuryansari Muharini
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.31514

Abstract

This research studied the dynamics model of breast cancer patients that was built as a dynamical system. The model had five compartments, including the subpopulations of stage 1 and 2 breast cancer patients, stage 3 cancer patients, stage 4 cancer patients, recovered individuals due to chemotherapy treatment, and patients who suffered cardiotoxicity. Equilibrium points and local stability were determined. The dynamical analysis resulted in one equilibrium point that exists and is stable under certain conditions. The model was constructed with the assumption that all patients undergo intensive chemotherapy treatment. This treatment caused side effects in the form of cardiotoxicity. Therefore, optimal control of additional treatment and ketogenic diet was applied. Additional treatment control is applied to prevent cardiotoxicity, while ketogenic diet control is used to reduce tumor cell growth. The aim of optimal control was to find out the treatment strategy that is effective in reducing cardiotoxicity and treatment costs. Numerical simulations were conducted to support the analysis results.
Obesity Prediction Using Synthetic Minority Oversampling Technique for Numeric and Continous and XGBoost Approaches Putri, Tiara Azahra Wika; Sa’adah, Umu; Habibah, Ummu
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.30818

Abstract

This study investigates the effect of using SMOTE-NC on the XGBoost algorithm in predicting obesity. The main objective of this research is to determine the effect of implementing SMOTE-NC and also the features that are most influential in the prediction process. By using the SMOTE-NC approach with XGBoost it is hoped that it can improve obesity prediction performance, data is collected from UCI Machine Learning for Obesity analysis. The prediction results reveal that the application of SMOTE-NC can improve the accuracy of obesity prediction using XGBoost. The results show that the best accuracy in this study was able to reach 98.30%. Further analysis, this research reviews several influential features in the prediction process, namely Weight, Height and Age. Based on these results, it is hoped that they can contribute to further research. Overall, this research underlines the importance of maintaining health to avoid obesity by keeping body weight within normal limits.
Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework Ardiana, Dita; Habibah, Ummu; Trisilowati, Trisilowati; Ranom, Rahifa Binti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41525

Abstract

This study investigates the numerical simulation of solitary wave propagation governed by the KdV-BBM equation using a robust Method of Lines (MOL) framework. The governing nonlinear equation is transformed into a system of ordinary differential equations through spatial discretization, and the performance of three temporal integration schemes is evaluated: the first-order Euler method, the fourth-order Runge-Kutta (RK-4), and the fifth-order iRK-5 method. Quantitative analysis using Mean Absolute Error (MAE) for various time steps (t = 0.2, 0.1, 0.05, and 0.01) reveals that the iRK-5 scheme provides enhanced temporal precision, achieving error magnitudes as low as 106 and consistently aligning with the exact traveling-wave solution. Notably, the iRK-5 method demonstrates greater algorithmic efficiency, achieving an accuracy level of 4.55 106 at a coarser time step of t = 0.1, whereas the RK-4 scheme requires a finer time step of t = 0.05 to reach the same precision. Both high-order methods eventually reach a spatial error floor where further temporal refinement yields no significant reduction in MAE, emphasizing that high-order temporal integration, particularly the iRK-5 scheme, is essential for preserving the physical integrity of complex nonlinear wave phenomena while maintaining optimal computational effort.
Co-Authors Angelina Renny Christin Octavia Sianturi Ardiana, Dita Cholifatul Maulidiah Ferreira, Tomas Goncalves Indah Yanti Mohamad Handri Tuloli Muhammad Abdurrahman Rois Mulya Lezani, Nadine Muniroh, Kunnisai Nielda Alifah Mulyanti Nurkarimah, Dwi Putri, Tiara Azahra Wika Rachman, Alifira Meliana Ranom, Rahifa Binti Rimanada, Viva Sa’adah, Umu Tomas Goncalves Ferreira Trisilowati Trisilowati, Trisilowati Trisilowati, Trisilowati Tuloli, Mohamad Handri Viva Rimanada Wuryasari Muharini Kusumawinahyu