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INDONESIA
Indonesian Journal of Applied Mathematics
Published by Institut Teknologi Sumatera
ISSN : 27742067     EISSN : 27742016     DOI : https://doi.org/10.35472/indojam
Core Subject : Economy, Science, Engineering,
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Physics
Indonesian Journal of Applied Mathematics is a scientific publication media that publishes articles from the results of research or studies in the field of applied mathematics, focusing on Computational Mathematics, Optimization, Actuarial, Statistics, Numerical Modelling, Mathematical Physics, Financial Mathematics and Combinatorics. This journal publish twice in a year April and October. Indonesian Journal of Applied Mathematics is fully supported by Mathematics Study Program and Actuarial Study Program of Institut Teknologi Sumatera.
Arjuna Subject : Matematika - Matematika Terapan
Articles 60 Documents
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Studi Komparatif Efisiensi Komputasi antara Metode Newton-Raphson dan Metode Bierge-Vieta pada Pencarian akar Polinomial Hafnani; Muna Irawan; T. Murdani Saputra; Taufiq Iskandar; Syarifah Meurah Yuni; Saiful Amri
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2450

Abstract

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: A Python library for symplectic pseudo-spectral solution of the idealized (1+1)D nonlinear Klein-Gordon equation Sandy Hardian Susanto Herho; Siti Kaban
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2537

Abstract

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; Dila Tirta Julianty; Fuji Lestari; Elifas Hani Christien; Nia Ahmadia Sumardi; Welson Tawan; Natalie Evangelista; Debra Carol Lin G.N.
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2716

Abstract

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; Angela Putri Larasati; Desi Wulandari; Robecca Miranda Agustina Gultom; Setia Hot Dameria Purba; Suci Ayu Pangestuti
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2728

Abstract

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; Ahmed Hasan Alridha
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2736

Abstract

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.
Perhitungan Cadangan Premi Asuransi Jiwa Berjangka Menggunakan Metode Premium Sufficiency Dan Metode Full Preliminary Term Dengan Tingkat Suku Bunga Hull White Cindy Faradilla; Tiara Yulita; Amalia Listiani
Indonesian Journal of Applied Mathematics Vol. 6 No. 2 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i2.2747

Abstract

In daily life, humans engage in various activities that can pose risks, such as death, accidents, and financial risks. Therefore, humans need to prepare themselves to face unexpected risks to avoid significant losses. Insurance is an effort that can be done to obtain protection from risks. Insurance companies, as the insurer, are required to set aside premium reserves to ensure the availability of funds to pay the insured's benefits in the event of a future claim. In this study, the Premium Sufficiency method and the Full Preliminary Term method were used to calculate premium reserves. Reserve calculations take place over a fairly long period, so it is necessary to consider interest rate fluctuations that occur due to economic activity. To model these fluctuations, the Hull-White interest rate model can be used. The purpose of this study is to determine the comparative analysis of the premium reserve values ​​​​from the two methods calculated using the Hull-White interest rate model. Based on the results obtained, the premium reserve value using the Premium Sufficiency method is greater than the Full Preliminary Term method. This is because the Full Preliminary Term method assumes that the first year's reserve is zero because it is used to cover costs.
Elliptic Curve Digital Signature Algorithm dan Secure Hash Algorithm-256 untuk Autentikasi Transaksi Berbasis PIN pada Aplikasi Mobile Banking Alvina Hardiyanti; Siti Fatimah; Rini Marwati
Indonesian Journal of Applied Mathematics Vol. 6 No. 2 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i2.2992

Abstract

Conventional security models in mobile banking applications remain vulnerable to the theft of Personal Identification Numbers (PINs) transmitted to the server. This research integrates the Elliptic Curve Digital Signature Algorithm (ECDSA) and Secure Hash Algorithm-256 (SHA-256) for more secure transaction authentication in mobile banking applications. The PIN is no longer sent to the server, but rather combined with the username and device ID to generate a private key using the Password-Based Key Derivation Function 2 (PBKDF2). The application prototype was built using the Python programming language with a client-server architecture. The client performs hashing on the transaction data using SHA-256 and signs it with ECDSA, while the server verifies the signature. The application's performance evaluation was conducted through three testing scenarios, namely normal transactions, access from unregistered devices, and transaction nominal manipulation. The test results indicate that the application is capable of executing signing and verification accurately across all scenarios. This proves that the applied method is effective in ensuring authentication security, data integrity, and non-repudiation in mobile banking transactions.Keywords: Authentication, Digital Signature, ECDSA, Mobile Banking, PBKDF2, PIN, SHA-256. Abstrak: Model keamanan konvensional pada aplikasi mobile banking masih rentan terhadap pencurian Personal Identification Number (PIN) yang dikirimkan ke server. Penelitian ini mengintegrasikan Elliptic Curve Digital Signature Algorithm (ECDSA) dan Secure Hash Algorithm-256 (SHA-256) untuk autentikasi transaksi yang lebih aman pada aplikasi mobile banking. PIN tidak lagi dikirimkan ke server, melainkan digabungkan bersama username dan device ID untuk membangkitkan kunci privat menggunakan Password-Based Key Derivation Function 2 (PBKDF2). Prototipe aplikasi dibangun menggunakan bahasa pemrograman Python dengan arsitektur klien-server. Klien melakukan hashing data transaksi menggunakan SHA-256 dan menandatanganinya dengan ECDSA, sementara server memverifikasi tanda tangan tersebut. Evaluasi kinerja aplikasi dilakukan melalui tiga skenario pengujian, yaitu transaksi normal, akses dari perangkat tidak terdaftar, dan manipulasi nominal transaksi. Hasil pengujian menunjukkan bahwa aplikasi mampu mengeksekusi penandatanganan dan verifikasi secara akurat pada seluruh skenario. Hal ini membuktikan bahwa metode yang digunakan efektif dalam menjamin keamanan autentikasi, integritas data, dan nirsangkal pada transaksi mobile banking.
Kontrol Optimal pada Model Predator–Prey dengan Respons Fungsional Holling Tipe II untuk Pengendalian Hama Berbasis Predator Alami Dewi Suhika; Nurul Indah Safitri; Nela Rizka
Indonesian Journal of Applied Mathematics Vol. 6 No. 2 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i2.2993

Abstract

Hama tanaman merupakan salah satu faktor utama yang dapat menurunkan produktivitas pertanian, sehingga diperlukan strategi pengendalian yang efektif, terukur, dan tetap mempertimbangkan keberlanjutan ekosistem. Penggunaan pengendalian kimia secara berlebihan dapat memberikan dampak negatif terhadap lingkungan dan organisme bukan sasaran, termasuk predator alami. Oleh karena itu, diperlukan pendekatan pengendalian yang mampu menekan populasi hama sekaligus menjaga keberadaan predator alami dalam sistem. Penelitian ini membahas model kontrol optimal pada dinamika interaksi hama dan predator alami dengan dua strategi pengendalian, yaitu pengendalian hama dan pelepasan predator alami. Model yang digunakan berbentuk sistem predator-prey dengan respons fungsional Holling tipe II. Fungsi tujuan dirancang untuk meminimumkan kepadatan hama, biaya pengendalian hama, biaya pelepasan predator alami, serta penalti terminal terhadap populasi hama pada akhir waktu simulasi. Prinsip Maksimum Pontryagin digunakan untuk memperoleh sistem optimalitas yang terdiri atas sistem state, sistem adjoint, syarat transversal, dan karakterisasi kontrol optimal. Selanjutnya, solusi numerik diperoleh menggunakan metode forward-backward sweep. Hasil simulasi menunjukkan bahwa penerapan dua kontrol optimal mampu menekan kepadatan hama secara signifikan. Pada akhir simulasi, kepadatan hama tanpa kontrol sebesar , sedangkan dengan dua kontrol optimal turun menjadi , atau mengalami penurunan sekitar . Selain itu, kepadatan predator alami dengan kontrol tetap bernilai positif sebesar , sehingga predator alami masih dapat dipertahankan dalam sistem. Nilai fungsi objektif juga menurun dari tanpa kontrol menjadi dengan kontrol. Dengan demikian, kombinasi pengendalian hama dan pelepasan predator alami efektif dalam menekan populasi hama dengan tetap mempertimbangkan biaya kontrol dan keberlanjutan predator alami.
PREDIKSI BANYAK HARI HUJAN DI KOTA JAMBI MENGGUNAKAN ALGORITMA RANDOM FOREST REGRESSION BERBASIS DATA IKLIM Ferdinand Manurung; Sherli Yurinanda; Sarmada
Indonesian Journal of Applied Mathematics Vol. 6 No. 2 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i2.3001

Abstract

Banyak hari hujan merupakan salah satu indikator klimatologi penting yang memengaruhi sektor pertanian, pengelolaan sumber daya air, serta mitigasi bencana hidrometeorologi. Variasi banyak hari hujan dipengaruhi oleh beberapa faktor klimatologi, antara lain curah hujan, kelembapan udara, suhu udara, dan LPM, yang memiliki hubungan kompleks dan nonlinier. Penelitian ini bertujuan untuk memprediksi banyak hari hujan di Kota Jambi menggunakan metode Random Forest Regression serta mengidentifikasi faktor-faktor klimatologi yang paling berpengaruh. Penelitian ini menggunakan data sekunder bulanan yang diperoleh dari Stasiun Meteorologi Kelas I Sultan Thaha Jambi pada periode 2018 hingga 2025 sebanyak 96 pengamatan. Metodologi penelitian meliputi eksplorasi data, penentuan hyperparameter menggunakan Grid Search dengan 5-Fold Cross Validation, pembangunan model Random Forest Regression, evaluasi model menggunakan RMSE dan R², serta analisis feature importance. Hasil penelitian menunjukkan bahwa model memperoleh nilai RMSE sebesar 2,769 dan R² sebesar 0,695 pada data testing, yang mengindikasikan bahwa model mampu menjelaskan 69,5% variasi banyak hari hujan dengan rata-rata kesalahan prediksi sekitar tiga hari. Analisis feature importance menunjukkan bahwa curah hujan merupakan faktor yang paling berpengaruh, diikuti oleh LPM, kelembapan udara, dan suhu udara. Temuan ini menunjukkan efektivitas Random Forest Regression dalam memodelkan hubungan klimatologi yang nonlinier serta memprediksi banyak hari hujan di Kota Jambi.
Evidence-First Data Management for Trustworthy AI: A Database Architecture for Ecological Tourism Intelligence Ardika Satria; Mika Alvionita S; Ira Safitri; Febri Dwi Irawati
Indonesian Journal of Applied Mathematics Vol. 6 No. 2 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 2 October Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i2.3029

Abstract

Multi-source operational data, in this study, tourism-village records from Indonesia’s national JADESTA portal is rarely stored with enough structure to support trustworthy artificial-intelligence consumption: values are overwritten, provenance is recorded per record rather than per attribute, and unverified data reaches downstream consumers indistinguishably from verified data. This paper proposes P1, a database-driven data management architecture that stores every attribute value as a claim carrying source, time, and confidence; accumulates corrections as new, non-destructive evidence events; computes a confidence score per claim; and enforces a policy gate before any value is published to an AI-facing semantic view. P1 is compared against two realistic baselines B0, an overwrite ETL pipeline, and B1, a record-level lineage pipeline on the full 21,461-record JADESTA corpus under five injected synthetic failure scenarios (duplicate, conflict, missing, late update, and schema drift), and against a 304-pair manually labelled gold sample (Cohen’s κ = 0.742) for entity-resolution quality. The results show that P1’s provenance is not merely nominally complete like B1’s but substantively so: B1 reports a provenance coverage of 1.000 yet a provenance precision of only 0.471, quantifying a "phantom provenance" gap that attribute-level claims avoid by construction. P1’s entity resolution achieves an F1 of 0.849 (precision 0.900, recall 0.804) on the merge decision, and its conservative refusal to auto-merge ambiguous record pairs is empirically justified in 78.6 per cent of the labelled pairs it deferred. P1’s policy gate reduces unverified data reaching the semantic view from 1.000 in both baselines, by construction, to 0.000. These gains carry a scale-dependent performance cost: P1 is approximately 151 times slower than B0 at 500 records, growing to approximately 5,447 times slower on the full corpus, traced to the quadratic per-block complexity of its entity resolution a concrete direction for future optimisation. The evaluation is scoped explicitly: entity-resolution quality claims cover the merge decision only, not the reject threshold, and policy-gate claims cover the gating mechanism only, not the calibration of the confidence function against independent ground truth. The data model, the confidence and policy contracts, and the evaluation protocol are architecture- and technology-independent, and the experiment code, gold sample, and raw results are released as a reproducible benchmark.

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