Jurnal Matematika, Statistika dan Komputasi
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Numerical Simulation of Thermal Newtonian Fluid Flow Driven by Horizontal Convection in A Porous Cavity
Full text linkAbstract
Horizontal convection is a distinct form of natural convection where flow is generated by uneven buoyancy along a horizontal boundary. This study presents a numerical simulation of horizontal convection within a porous rectangular cavity. The flow is driven by a non-uniform heating on the top surface, while the other boundaries are thermally insulated. We derive a governing equation involving four dimensionless parameters: the Darcy number, the Rayleigh number, the viscosity ratio, and the geometric aspect ratio. This equation is solved numerically through the finite difference method. Our investigation emphasizes how the Rayleigh number and viscosity ratio influence the flow of the thermal fluid. The results show that viscosity inhibits convection, thereby weakening the thermal boundary layer
Nonlinear Robust Sliding Mode Control for Measles with Parameter Uncertainties
Full text linkMeasles is a highly contagious viral disease that persists as a global threat following its resurgence in 2018–2019. The SVEIR epidemic model is considered to represent the dynamics of measles. Various factors affecting the spread of measles result in uncertainties and imprecision in the modelling of measles, thereby a robust control strategy is required to eradicate the disease. The aim of the study is to design a nonlinear robust sliding mode control to drive the number of individuals exposed to or infected with measles to zero through a targetted tracking scheme, despite uncertainties in measles dynamics. This is achieved by administering treatments to exposed and infected individuals while maintaining the existing levels of vaccination. The proposed control strategies have been proven to achieve the tracking objective analytically by employing Lyapunov\u27s stability theorem and Barbalat\u27s Lemma. Employing an adaptive switching gain that is updated online during the design process eliminates the necessity of prior information on the bounds of model uncertainties. Numerical simulations of different cases involving parameter uncertainty and diminishing rates were carried out to evaluate control performance. Using a saturation function and a tangent hyperbolic function instead of a sign function in the controllers and adjusting the rate of switching gain updating can reduce chattering incidents arising from the implementation of sliding mode control. Within the nine cases of parameter uncertainties considered, the robust sliding mode control strategy is effective in eradicating the disease, with average reductions in the number of exposed and infected individuals of 80.82–81.57% and 81.01–84.18%, respectively
The Best Model of the Autoregressive Integrated Moving Average (ARIMA) Method for Predicting the Exchange Rate of the Indonesian Rupiah Against the US Dollar (USD) for the Period July 2025 - June 2026
Full text linkThe exchange rate fluctuations are an important indicator that affects the stability of a country\u27s economy, including Indonesia. This condition makes accurate exchange rate forecasting a strategic necessity in supporting economic decision-making and fiscal policy. One of the methods widely used for exchange rate forecasting is Autoregressive Integrated Moving Average (ARIMA), which has proven effective in capturing patterns and trends in historical data. Therefore, this study was conducted to find the best model for forecasting the exchange rate of the Rupiah against the US Dollar (USD) using the Autoregressive Integrated Moving Average (ARIMA) method. The data used is monthly data on the exchange rate of the Rupiah against the USD for the period January 2015 to June 2025. By identifying, estimating, and diagnosing the model, the best ARIMA model was obtained that met the white noise assumption and produced the lowest AIC/BIC value
Survival Analysis Of Diabetes Mellitus At RSUP Dr. Tadjuddin Chalid Makassar
Full text linkDiabetes mellitus (DM) is a metabolic disorder characterized by hyperglycemia and disturbances in the metabolism of carbohydrates, fats, and proteins, resulting from an absolute or relative deficiency in insulin secretion or action. The prevalence of DM in Indonesia continues to rise, reaching 2.2% in 2023. In South Sulawesi, Makassar City exhibits a particular urgency with a prevalence of 2.14%, a figure significantly exceeding the provincial average. This study aims to determine the survival probability of inpatients with diabetes mellitus at RSUP Dr. Tadjuddin Chalid Makassar using the Kaplan-Meier method. Based on the analysis, the results indicate that the survival probability of hospitalized diabetes mellitus patients is 0.649 or 64.9%.
Keywords: Survival Analysis, Kaplan-Meier, Diabetes Mellitu
Forecasting The Price of Red Bird\u27s Eye Chili in Southeast Sulawesi Province Containing Outlier Data Using ARIMA Method with Iterative Procedure
Full text linkThe price of red bird\u27s eye chili in Southeast Sulawesi Province often experiences fluctuations that are detrimental to farmers. This study aims to forecast the price of red bird\u27s eye chili using the ARIMA model and to correct outliers that affect the model’s accuracy. The ARIMA(2,1,1) model was selected as the best-fitting model after detecting and correcting four innovational outliers (IO). The correction process resulted in a decrease in the Mean Squared Error (MSE) from 50,602,363 to 38,245,864. The 20-week-ahead forecast indicates a downward trend in prices, with increasingly stable prediction intervals. This method proves effective in improving model accuracy and providing more reliable information for decision-making
Zero-Inflated Integer Autoregressive (ZINAR) Approach in Modeling Major Earthquakes in Sumatra Region
Full text linkSumatra is one of the regions in Indonesia with the highest seismic activity due to the convergence of the Indo-Australian and Eurasian plates. Major earthquakes with magnitudes of more than 7 pose serious risks, making it essential to understand their frequency for effective disaster mitigation planning. This study aims to model the frequency of major earthquakes in Sumatra using the Zero-Inflated Integer Autoregressive (ZINAR) model, which accommodates discrete data with excess zeros and temporal dependence. The analysis indicates significant overdispersion and zero inflation, leading to the selection of the ZINAR model as the most suitable approach compared to alternative models such as INAR, NB-INAR, and NB-ZINAR. The ZINAR model demonstrates superior performance in capturing the occurrence patterns of large earthquakes and effectively identifies non-event periods, although its predictive accuracy for actual event timing remains limited. Overall, the ZINAR model proves effective for modeling complex earthquake data and provides valuable insights to support disaster mitigation efforts in the Sumatra region
Actuarial Estimation of Unit-Linked Insurance Benefits Using the Point-to-Point Method with De Moivre’s Law
Full text linkUnit-linked insurance is a life insurance product that combines elements of protection and investment. Hence, the value of the benefits received by policyholders depends on the performance of the underlying investment asset. This study aims to estimate the benefits of a dual-purpose life insurance (endowment) unit-linked policy using the Point-to-Point method and De Moivre\u27s Law. The Point-to-Point method determines investment results based on changes in stock prices from the beginning to the end of the contract period. At the same time, De Moivre\u27s Law is applied to calculate the insured\u27s chances of life and death to determine actuarial benefits. The data used are daily share prices of PT Bank Negara Indonesia Tbk for the period July 2024-June 2025, assuming a risk-free interest rate of 5,25%. The results showed that the stock volatility of 0,378 reflected a moderate level of risk, while the endowment life insurance benefit obtained of 1,43061 resulted in a single premium of IDR 66.809.378. The investment benefits received by the heirs are calculated based on the benefit structure with a minimum warranty limit and a predetermined maximum value (cap). These findings show that the Point-to-Point method provides a transparent, easy-to-understand estimate of benefits and can be a relevant alternative for calculating the value of unit-linked endowment insurance products in Indonesia
European Option Pricing Using Trinomial Method with Dividend
Full text linkThe accurate valuation of European options is a primary challenge in quantitative finance, particulary when dividend payment influence the underlying stock price. Convetional option pricing models often overlook the dividend variable or face computational complexities that reduce the accuracy and stability of the result. This study aims to determine the value of Eropean-style options using the trinomial method with dividend payments. The trinomial method with dividend was applied to five stock with the same period and expiration date. Based on the Mean Absolute Percentage Error (MAPE) calculation, it can be concluded that the trinomial model used to predict option prices has varying levels of accuracy. The result show the MAPE values for a 2.25 month dividend as follows: AAPL at 27.11% for calls and 25.86% for puts; MSFT at 10.03% for calls and 4.57% for puts; AON at 7.56% for calls and 6.52% for puts; IBM at 24.96% for calls and 15.22% for puts; and META at 17.46% for calls and 28.59% for puts. Meanshile, the MAPE calvulation for a 3 month dividend yielded: AAPL at 27.13% for call and 25.86% for puts; MSFT at 10.03% for calls and 4.57% for puts; AON at 7.94% for calls and 7.69% for puts; IBM at 24.96% for calls and 15.22% for puts; and META at 17.46% for calls and 28.59% for puts. Oevrall, the calculations show aggregate MAPE values of 17.42% for calls and 16.15% for puts (2.25 month dividend), and 17.50% for calls and 16.39% for puts (3 month dividend). This indicates that the trinomial model, which accounts for distributions, produces values thah approximate actual option prices
Evaluation of Waterpark Performance Using Distance Measure on Pythagorean Fuzzy Sets
Full text linkThe rapid growth of the tourism industry, particularly in waterparks, necessitates a comprehensive evaluation to enhance customer satisfaction and competitiveness. This study aims to evaluate the performance of waterparks in Manado City using the Distance Measure method on Pythagorean Fuzzy Sets (PFS). Data were collected through questionnaires from 100 visitors across four waterparks: Lomban, Mercy, Citraland, and Paradise. The findings reveal that Citraland Waterpark achieved the highest relative similarity score of 0.5234, followed closely by Lomban Waterpark at 0.51990 and Mercy Waterpark at 0.51949, while Paradise Waterpark ranked last with a score of 0.4762. Further analysis indicates that Citraland Waterpark excels in nearly all evaluation attributes, including service quality and cleanliness. This research demonstrates the effectiveness of applying Distance Measure on PFS in addressing uncertainties in subjective customer assessments, providing valuable insights for waterpark managers to enhance service quality. Future research is recommended to expand the study to include additional waterparks and evaluation attributes for a more comprehensive analysis
Modeling the Percentage of Poor Population in West Sumatra in 2024 Using Nonparametric B-Spline Regression
Full text linkPoverty is a multidimensional issue and remains a major challenge in West Sumatra Province. This study analyzes the percentage of the poor population in 2024 using a nonparametric B-Spline regression approach with the independent variables being the percentage of per capita expenditure on food, the labor force participation rate, and the average length of schooling. Data are sourced from the official publication of the Central Statistics Agency of West Sumatra Province in 2024. The results show that the best model is obtained from the second-order B-Spline regression with one node for each independent variable, based on the minimum Generalized Cross Validation (GCV) value. This model produces a coefficient of determination of 92.46% and a Mean Absolute Percentage Error (MAPE) of 11.02%, indicating high prediction accuracy. Substantively, the average length of schooling has a negative effect on the poverty rate, while food expenditure and labor force participation have varying effects across regions. These findings indicate that B-Spline regression is effective in capturing nonlinear and complex relationships between socioeconomic variables, but its interpretation still needs to consider the empirical context in the field