Indonesian Journal of Computational and Applied Mathematics
Indonesian Journal of Computational and Applied Mathematics covers a broad spectrum of topics at the intersection of mathematics, computation, and applied research. We invite submissions in areas such as: 1. Mathematical Modeling and Simulation Mathematical modeling and simulation involve developing mathematical frameworks to represent real-world systems and using computational methods to analyze their behavior under various conditions. This interdisciplinary research integrates mathematical theories, numerical algorithms, and computer simulations to study complex physics, engineering, biology, and economics phenomena. Models can be deterministic or stochastic, relying on differential equations, statistical methods, or machine learning techniques. Simulations enable researchers to predict outcomes, optimize processes, and test hypotheses in a controlled virtual environment, reducing experimental costs and risks while enhancing scientific understanding and technological innovation. 2. Computational Algorithms and Optimization Research in Computational Algorithms and Optimization focuses on developing efficient algorithms to solve complex mathematical and real-world problems by optimizing resource use, computation time, and accuracy. This field integrates techniques from numerical analysis, machine learning, operations research, and high-performance computing to tackle challenges in diverse domains such as engineering, finance, logistics, artificial intelligence, and scientific simulations. Key areas of study include convex and non-convex optimization, metaheuristic algorithms (e.g., genetic algorithms, particle swarm optimization), combinatorial optimization, and large-scale data-driven approaches. Advancements in this field enable faster and more precise decision-making, improving efficiency in the healthcare and transportation industries. 3. Numerical Methods and Scientific Computing Numerical Methods and Scientific Computing is a field that focuses on developing, analyzing, and implementing algorithms to solve mathematical problems that arise in science and engineering. It combines mathematical theory, computational techniques, and software development to approximate solutions for complex problems that may not have analytical solutions, such as differential equations, optimization, linear algebra, and data-driven modeling. This field is crucial in simulations, data analysis, and large-scale computations across various disciplines, including physics, engineering, finance, and machine learning. Advances in numerical methods enhance the accuracy, stability, and efficiency of computational models, enabling researchers to tackle real-world problems that are computationally intensive. 4. Machine Learning and AI in Mathematics "Machine Learning and AI in Mathematics" is an interdisciplinary field that leverages artificial intelligence techniques, particularly machine learning, to solve mathematical problems, discover new patterns, and enhance computational efficiency. It encompasses applications such as symbolic reasoning, theorem proving, optimization, and numerical analysis, enabling AI to assist in conjecture generation, equation solving, and high-dimensional data modeling. Machine learning methods, including neural networks and reinforcement learning, are increasingly used to automate mathematical proof verification and explore unsolved problems. This synergy between AI and mathematics advances pure and applied mathematics and drives progress in physics, engineering, and data science. 5. Financial Mathematics and Quantitative Economics Financial Mathematics and Quantitative Economics is an interdisciplinary field that applies mathematical models, statistical techniques, and computational methods to analyze and solve complex problems in finance and economics. It encompasses risk management, asset pricing, portfolio optimization, derivative pricing, and econometrics, using tools from probability theory, stochastic processes, and optimization. This field is crucial for data-driven financial markets, banking, insurance, and economic policy decisions. Integrating advanced quantitative methods with economic theory enables professionals to model financial systems, assess risks, and develop investment and economic growth strategies. 6. Data Science and Statistical Applications Data Science and Statistical Applications involve using mathematical and computational techniques to extract insights, make predictions, and inform decision-making from structured and unstructured data. Data science integrates statistics, machine learning, programming, and domain knowledge to analyze large datasets, uncover patterns, and develop predictive models. Statistical applications provide the theoretical foundation for data analysis, ensuring rigor in hypothesis testing, probability modeling, and inferential statistics. They drive healthcare, finance, marketing, and artificial intelligence advancements, enabling data-driven decision-making and innovation across industries. 7. Mathematical-based Signal and Image Processing Mathematical-based Signal and Image Processing involves applying advanced mathematical techniques to analyze, manipulate, and interpret signals and images for various engineering and scientific applications. It leverages concepts from linear algebra, Fourier analysis, wavelet transforms, probability theory, and optimization to enhance signal clarity, compress data, detect patterns, and extract meaningful information. This approach is fundamental in medical imaging, telecommunications, remote sensing, and artificial intelligence, where precise and efficient processing of signals and images is crucial for decision-making, automation, and technological advancements. 8. Computational Mechanics and Engineering Applications Computational Mechanics and Engineering Applications is an interdisciplinary field that integrates numerical methods, physics-based modeling, and computer simulations to analyze and solve complex engineering problems. It encompasses finite element analysis (FEA), computational fluid dynamics (CFD), structural mechanics, material modeling, and multi-physics simulations. By leveraging high-performance computing, artificial intelligence, and data-driven techniques, this field enables the optimization and innovation of engineering designs across various industries, including aerospace, automotive, civil engineering, and biomedical engineering. Advances in computational mechanics enhance predictive capabilities, improve efficiency, and support the development of next-generation engineering solutions. 9. Bioinformatics and Computational Biology Bioinformatics and Computational Biology are interdisciplinary fields that combine biology, computer science, mathematics, and statistics to analyze and interpret biological data. Bioinformatics focuses on developing algorithms, databases, and computational tools to manage and process large-scale biological datasets, such as genomic sequences and protein structures. Conversely, computational biology involves modeling and simulating biological systems to understand complex biological processes, such as gene regulation and protein interactions. Together, these fields play a crucial role in advancing research in genomics, drug discovery, personalized medicine, and systems biology by leveraging computational techniques to uncover insights from biological data.
Articles
10 Documents
The Occurrence of a Neimark-Sacker Bifurcation on a Discrete-Time Predator-Prey Model Involving Fear Effect and Linear Harvesting
Kasim, Ranan;
Panigoro, Hasan S.;
Rahmi, Emli;
Nuha, Agusyarif Rezka;
Arsal, Armayani
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i1.5
This study investigates the dynamics of a discrete-time predator-prey model incorporating the fear effect and linear harvesting. The model assumes that both prey and predator populations are harvested proportionally to their densities, while the growth rate of the prey population is negatively impacted by predator presence due to fear. The analytical exploration identifies three fixed points: the extinction point, the predator-free equilibrium, and the coexistence equilibrium. Stability analysis and numerical simulations confirm the occurrence of a Neimark-Sacker bifurcation at the interior equilibrium, demonstrating the model's complex dynamical behaviors. The findings provide insights into population sustainability under different harvesting and predation conditions, highlighting how fear and harvesting jointly influence ecosystem stability.
Application of the Monte Carlo Method to Pricing Lookback Fixed Option with Stochastic Volatility
Hidayanti, Sri Amalia;
Rahmi, Emli;
Yahya, Lailany
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i1.6
Options are a derivative product that trades the right to call and put on an asset at a certain price and during an agreed time. Determining the optimal option price is often difficult due to changes in stock prices. One model that can be used to calculate the price of Lookback Fixed options is the Monte Carlo Method with stochastic volatility of the Heston model, with parameter estimation using Ordinary Least Squares (OLS), and Euer-Maruyama and calculation of the effect of initial stock price, strike, and maturity time. The estimated stock price is then used to calculate the Lookback Fixed option price using the Monte Carlo method. The research results obtained good results with a fairly small error rate. In addition, the analysis of the effect of strike price, strike, and maturity time shows results consistent with option pricing theory.
Particle Swarm Optimization-Enhanced DBSCAN for Clustering Malnutrition Data on Java Island, Indonesia
Nurafni, Firda;
Nashar, La Ode;
Panigoro, Hasan S.
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i1.7
This manuscript proposes an approach that uses the Particle Swarm Optimization (PSO) algorithm to optimize the parameters of the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) method in mapping the spatial pattern of malnutrition in Java. Results showed that with a Silhouette Coefficient value close to 1 (0.134) and the lowest Davies-Bouldin Index (1.80), PSO successfully determined the optimal epsilon (eps) value of 1.76 and the optimal minimum number of points of 3. Index validation showed that DBSCAN could map the study area into three clusters that reflected the level of malnutrition, where 82 districts/cities were included in Cluster 0, 5 districts/cities in Cluster 1, and 3 districts/cities in Cluster 2. In contrast, 29 districts/cities were identified as noise. This finding confirms that the PSO approach in optimizing DBSCAN parameters can improve the method's effectiveness in handling complex cases such as malnutrition in a geospatial context.
Implementation of Fuzzy Time Series Markov Chain Method using Kernel Smoothing in forecasting the Stock Price of PT. Elnusa Tbk.
Mokodompit, Marcela;
Nasib, Salmun K;
Djakaria, Ismail;
Yahya, Nisky Imansyah;
Hasan, Isran K.
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i1.9
This research aims to apply the Fuzzy Time Series Markov Chain combined with Kernel Smoothing in forecasting stock prices. The Kernel Smoothing technique is used to smooth stock data before the fuzzification process, resulting in more accurate predictions. The research stages include Data Smoothing, Fuzzy interval formation, Fuzzy Logical Relationship and Fuzzy Logical Relationship Group formation, and forecasting using Markov Chain Transition Matrix. Evaluation using MAPE shows a low prediction error rate, with a value of 0.005974257%, so this method is effective for volatile stock data. The implementation of this model is expected to be a reference for investors and analysts in understanding and predicting future stock price movements.
A Mathematical Model of the Mud Crab (Scylla Sp.) Involving Cannibalism and Refuge
Abubakar, Agung Sucipto;
Panigoro, Hasan S.;
Djakaria, Ismail;
Nuha, Agusyarif Rezka;
Hasan, Isran K.;
Asriadi, Asriadi
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 1: February 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i1.12
Cannibalism, a common ecological phenomenon in various species, significantly impacts the population dynamics of mud crabs (Scylla sp.). This study develops a mathematical model to analyze the effects of cannibalism and protective refuges on the population sustainability of juvenile and adult mud crabs. The model identifies two equilibrium points: the extinction equilibrium and the coexistence equilibrium. Stability analysis using the Jacobian matrix reveals that the extinction equilibrium is locally asymptotically stable under specific conditions. In contrast, the coexistence equilibrium depends on the transition rate from juvenile to adult crabs and the effectiveness of protective measures. Numerical simulations demonstrate that increasing the transition rate and implementing higher levels of refuge protection mitigate the adverse effects of cannibalism, enhancing population stability. These findings provide a quantitative foundation for sustainable fisheries management and conservation strategies for mud crab populations in mangrove ecosystems.
Dynamics of Alcohol Consumption Model with Public Awareness and Saturated Incidence
Beay, Lazarus Kalvein;
Saija, Maryone;
Rijoly, Monalisa E.;
Lesnussa, Yopi Andry;
Talakua, Mozart Winston;
Ilwaru, Venn Yan Ishak
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i2.14
This article develops a mathematical model for studying the impact of public awareness and intervention strategies on alcohol consumption patterns. To protect populations from addiction, we are focusing on educational campaigns and interventions. Alcohol consumption cases decrease as the model variable awareness susceptible class is increased through awareness campaigns and interventions. The nonnegativity and boundedness of the model's solutions are analyzed. A qualitative analysis of the model's equilibrium points and the alcohol reproductive number, R0, was performed. Global stability was analyzed for alcohol consumption at the positive equilibrium point via a suitable Lyapunov function. When the alcohol reproductive number (R0) is less than one, the alcohol-free equilibrium is globally asymptotically stable; otherwise, it is unstable. Although educational campaigns protect vulnerable people, their impact on the model is substantial. The simulation shows that the intervention directly and drastically reduces the target alcoholic population.
Developing a Python-Based Application for a Discrete-Time Population Dynamics Model
Nadhilah, Farhah;
Panigoro, Hasan S.;
Arsal, Armayani;
Nurwan, Nurwan;
Wungguli, Djihad;
Hasan, Isran K.
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i2.20
Difference equation is a type of equation in mathematics that is widely used to describe certain phenomena as time changes, one of which is in the field of population dynamics. In various studies, it is explained that solving complex population dynamics models is by using numerical simulations. Along with the development of technology, computational science is used to help solve mathematical problems that are difficult to solve analytically. One of them is to use a programming language, such as Python, to help present data in a graphical form. This research aims to develop an application that presents a computational solution to a difference equation using Python. The numerical results begin by entering the equation and variable values into the application, which then automatically generates a figure according to the entered equation. The figures generated in the application include one-dimensional and two-dimensional time series, as well as a Bifurcation diagram.
Dynamic Analysis of the Modified Leslie Gower Model with Harvesting of Prey and Holling Type II Functional Response
Eghary, Nabila Kholifatul Yuniar;
Savitri, Dian
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i2.32
This article studies the Modified Leslie-Gower model with constant business harvesting on the prey and functional response of Holling Type II. This approach is more realistic in several phenomena, one of which is in the phenomenon of rice fields, jali snakes, and owls. The research method begins by determining the assumptions for constructing models, stability analysis, and numerical simulations. Analysis of the equilibrium points was carried out to determine the condition of its stability locally using the Jacobian approach and the Routh-Hurwitz criteria by obtaining five existing points. Analysis of stability using the Jacobian matrix shows that the equilibrium point is an asymptotic node in certain conditions. Numerical simulations are carried out to determine the suitability of the results of the analysis using the software Maple and Python. Numerical simulation results show differences in the value of environmental carrying capacity affect changes in system solutions. Thus, the change in the value of carrying capacity does not always produce the same stability because the stability of the system depends on the sensitivity of the parameter to the overall dynamic structure. This finding provides a foundation for the management of biological resources, especially in controlling harvesting so that the population remains balanced.
Analysis of a Predator-Prey Model incorporating Prey Cannibalism and Intraspecific Competition on Predator
Biduli, Meiske;
Rahmi, Emli;
Nasib, Salmun K.
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i2.33
In this research, we formulated a predator-prey model by considering cannibalism in the prey and intraspecific competition on predator population. We found three types of equilibrium points existed under certain condition, except the extinction of all population equilibrium point. Further, we analyzed the local stability of each equilibrium point via linearization method. We found that the extinction of all population equilibrium point is always unstable and the other points locally asymptotically stable under some conditions. Finally, the numerical simulation carried out to verify the analytical results and to perform the impact of prey cannibalism rate.
Dynamic Analysis of an Ecological Model with Fear Effect on Prey and Additional Food for Predator Using Ratio-Dependent Functional Response
Salsabillah, Atiyah Safitri;
Savitri, Dian
Indonesian Journal of Computational and Applied Mathematics Vol. 1 No. 2: June 2025
Publisher : Gammarise Publishing
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DOI: 10.64182/indocam.v1i2.34
This study discusses the dynamic analysis of a predator-prey model that incorporates the fear effect on prey and supplemental food for predators, using a ratio-dependent functional response. The fear effect reduces the prey’s intrinsic growth rate due to behavioral changes under predation risk, while supplemental food enables the predator to survive even when prey density is low. The analysis begins with the formulation of the model equations, followed by the identification of equilibrium points, linearization of the system, and local stability analysis using eigenvalues. Numerical simulations are carried out using \textit{Matcont} and \textit{Pplane} to verify the analytical results and to illustrate the system’s qualitative behavior. The model parameters are based on the interaction between elk (\textit{ELK}) as prey and wolves (\textit{Canis lupus}) as predators. The results reveal four equilibrium points: $E_0=(0,0)$ is an unstable nodal source, $E_1=\left(0,\dfrac{nA(c\gamma - e\alpha)}{em}\right)$ and $E_2=\left(\dfrac{r-a}{b},0\right)$ are unstable saddle points, while the coexistence equilibrium $E_3=(x^*, y^*)$ is a stable spiral sink under certain parameter conditions. Bifurcation analysis with respect to the fear parameter $f$ and the supplemental food parameter $A$ reveals the occurrence of a transcritical bifurcation, where two equilibrium branches exchange stability. The system tends toward the equilibrium point $E_1$ when either $f$ or $A$ exceeds a critical threshold, indicating that predators can persist even as prey populations decline significantly. These findings suggest that predator survival is not solely dependent on prey availability but also influenced by the availability of alternative food sources and the intensity of the prey’s fear response.