Indonesian Journal of Applied Mathematics

Studi Komparatif Efisiensi Komputasi antara Metode Newton-Raphson dan Metode Bierge-Vieta pada Pencarian akar Polinomial

Hafnani — 2026-04-30

The Newton-Raphson method is a commonly used numerical method for finding polynomial roots, but its computational efficiency can be a concern. This paper compares the computational efficiency of the Newton-Raphson and Birge-Vieta methods by analyzing their computational time. Both methods have similar convergence rates and complexity. For low-degree polynomials ( ), the Newton-Raphson method shows faster computational time. This is likely due to the larger algorithmic overhead of the Birge-Vieta method.

amangkurat

Sandy Hardian Susanto Herho — 2026-04-30

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1 + 1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library’s capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

Penentuan Nilai Premi Asuransi Pertanian Berbasis Indeks Curah Hujan Dengan Metode Simulasi Stochastic Weather Generator Menggunakan Distribusi Weibull

Giandito Iskandar — 2026-04-30

The agricultural sector is vulnerable to various risks, which can lead to losses, such as rice farming that is susceptible to unstable rainfall. Therefore, agricultural insurance is needed to protect farmers from losses due to reduced harvests caused by various risks. The maximum value covered by the insurance company, called the indemnity value, reflects the total losses experienced by the farmers based on the average rice production yield. The average rice production yield is calculated using the estimated selling price obtained from the value- at-risk method amounting to IDR7,401,647.28/ton. This study aims to determine the premium that farmers must pay using a rainfall index value simulated using the Weibull Distribution with the Stochastic Weather Generator method. The result of this study is that the premium ranges from IDR143,567.5 – IDR11,511,142 or around 0.349% to 27.939% of the indemnity value amounting to IDR41,375,333.65.

Dinamika dan Probabilitas Transisi Curah Hujan Harian di MKG Itera Menggunakan Model Rantai Markov

Triyana Muliawati — 2026-04-30

This study aims to analyze the characteristics of daily rainfall in the Meteorology, Climatology, and Geophysics (MKG) Itera region during the period from January to October 2025 using a Markov Chain model. Daily rainfall data are classified into four states based on rainfall intensity, namely No Rain, Light Rain, Moderate Rain, and Heavy Rain. The analysis begins with descriptive statistics to identify general characteristics of the data. The average daily rainfall is 6.50 mm/day, with the highest recorded intensity reaching 82.8 mm on February 21, 2025, and a rainfall variance of 195.68 mm². Subsequently, a transition probability matrix is constructed to model the dynamics of rainfall condition changes between states from day to day. In addition, the steady-state probabilities are calculated to determine the long-term tendencies of rainfall conditions. The results indicate that daily rainfall exhibits a fluctuating pattern with relatively high variability. Most observations fall into the No Rain (48%) and Light Rain (40%) states, indicating that more than 88% of rainfall conditions are of low intensity. The transition probability matrix shows that the highest transition probability occurs from Moderate Rain to Light Rain at 66.7%, suggesting that moderate rainfall tends to decrease to light rainfall on the following day. Furthermore, the probabilities of remaining in the No Rain and Light Rain states are relatively high, at 61.1% and 46.7%, respectively, indicating persistence in dry or low-intensity rainfall conditions. The steady-state distribution shows that, in the long run, the probabilities are 47.6% for No Rain, 40.4% for Light Rain, 8.9% for Moderate Rain, and 3.0% for Heavy Rain. These findings suggest that rainfall patterns in the MKG Itera region are predominantly characterized by dry to low-intensity conditions. Overall, the Markov Chain model is capable of effectively representing the dynamics of daily rainfall and provides a comprehensive description of long-term rainfall characteristics in the MKG Itera region.

Reliability Analysis of Complex Systems: An Improved Risk Importance Measure Approach

Ekhlas Annon Mousa — 2026-04-30

This paper develops a new feature of the risk achievement worth (RAW) measure to expand its application to complex transportation directed networks, rather than being limited to traditional or undirected networks. The idea is to combine the RAW measure with modern techniques using the NetworkX library in Python, to improve its computational capabilities and handle complex directed networks efficiently. The approach was applied to a complex system . We calculated its reliability using a polynomial approach based on minimal paths and minimal cut sets, in addition to calculating the probability of path success and the probability of failure for cut sets. To demonstrate the effectiveness of the risk achievement worth measure, it was compared with the Birnbaum measures for analyzing the importance of network components at a default value of R = 0.60. The results showed complete consistency in terms of the importance levels of both measures, as confirmed by the Spearman correlation coefficient, with a value . Developing the risk achievement worth for analyzing complex networks is crucial to overcoming the computational complexity of the Birnbaum measure, which relies on differentials, unlike the RAW measure, which relies on simplified arithmetic procedures independent of differentials. Therefore, this provides an enables rapid identification of critical vulnerabilities in large-scale infrastructures.