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All Journal Interval: Indonesian Journal of Mathematical Education
Al-Moders, Ali Hussein
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Education Mathematics

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Dynamic Analysis and Stability Evaluation of a Discrete Mathematical Model for Flying Fox String Vibrations Matsubah, Aniq Nur; Al-Moders, Ali Hussein; Pantino, Francis; Anda, Asgar
Interval: Indonesian Journal of Mathematical Education Vol. 3 No. 1 (2025): June
Publisher : Cahaya Ilmu Cendekia Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37251/ijome.v3i1.1576

Abstract

Purpose of the study: This study aims to find the stability of changes in string deflection and the angle of string deflection when an object is launched along a flying fox. Methodology:This study uses a model developed by Kusumastuti et al. (2017). There are two models analyzed, namely the discrete model of the string deviation y(t) and the angle of the string deviation θ(t). The analysis steps include model reduction, model discretization, model linearization, fixed point search, and stability analysis. Stability is analyzed based on the eigenvalues ​​it has. Main Findings:Based on the research conducted, the following eigenvalues ​​were obtained: λ1 = -0.005h + (0.14565h)i, λ2 = -0.005h - (0.14565h)i, λ3 = -0.005h + (0.1331480769h)i, and λ4 = -0.005h - (0.1331480769h)i. The results of the study indicate that the system is in a stable condition (sink) because all eigenvalues ​​obtained are complex numbers with negative real parts. Thus, it can be concluded that the rope deflection, rope deflection velocity, rope deflection angle, and rope deflection angular velocity are in a stable condition. Novelty/Originality of this study: This study provides a new contribution to the understanding of discrete system dynamics in flying fox string vibrations, by showing that the stability of the system can be analyzed through the negative complex eigenvalues ​​generated from the model.
Modeling the Spruce Budworm Population: A Numerical Approach Using Heun and Runge-Kutta Methods Al-Moders, Ali Hussein; Pantino, Francis; Anda, Asgar
Interval: Indonesian Journal of Mathematical Education Vol. 3 No. 1 (2025): June
Publisher : Cahaya Ilmu Cendekia Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37251/ijome.v3i1.1583

Abstract

Purpose of the study: The purpose of this study is to determine the numerical solution of the spruce caterpillar model using the Heun method and the Third Order Runge-Kutta method, as well as to analyze the errors associated with both methods. Methodology: The type of research used in this study is library research. In this study, the data will be analyzed numerically from the data entry stage, data processing and results. The results obtained are from the Heun programming method and the Runge iteration method that have been determined previously. Kutta-Order Three will produce data with the smallest error in the number of. Main Findings:The results of the study showed the solution of the Pinus Lice model for the initial values ​​of B(t₀) = 2, S(t₀) = 10 cm, E(t₀) = 2 cm, at t = 5 years, with h = 0.05. Using the Heun method, it was obtained that B ≈ 3, S = 14.9058 cm, and E = 1.0047 cm, while the Third Order Runge-Kutta method produced B ≈ 3, S = 14.9057 cm, and E = 1.0046 cm. The error calculation showed that the B error was smaller with the Heun method, while the S and E errors were smaller with the Third Order Runge-Kutta method. Novelty/Originality of this study: The novelty of this study lies in the comparative analysis of the errors of the Heun Method and the Third Order Runge-Kutta Method in modeling the dynamics of spruce budworm populations with specific biological parameters.
Co-Authors Anda, Asgar Matsubah, Aniq Nur Pantino, Francis