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Limits: Journal of Mathematics and Its Applications

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Published by Institut Teknologi Sepuluh Nopember Surabaya

ISSN : 1829605X EISSN : 25798936 DOI : -

Core Subject : Science, Education,

Computer Science & IT Mathematics

Limits: Journal of Mathematics and Its Applications merupakan jurnal yang diterbitkan oleh Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Limits menerima makalah hasil riset di semua bidang Matematika, terutama bidang Analisis, Aljabar, Pemodelan Matematika, Sistem dan Kontrol, Matematika Diskrit dan Kombinatorik, Statistik dan Stokastik, Matematika Terapan, Optimasi, dan Ilmu Komputasi. Jurnal ini juga menerima makalah tentang survey literatur yang menstimulasi riset di bidang-bidang tersebut di atas.

Arjuna Subject : Matematika - Matematika Terapan

Articles 267 Documents

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Perbandingan Metode GARCH, LSTM, GRU, dan CNN pada Peramalan Volatilitas Kurs Septiani, Adeline Vinda; Afendi, Farit Mochamad; Kurnia, Anang
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 1 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i1.3384

Currency volatility is an important aspect of time series data analysis in economics and finance. This study aims to compare the performance of four methods: Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Convolutional Neural Network (CNN), in predicting the volatility of the Rupiah against the US Dollar. The data used is daily exchange rates from January 2015 to March 2024. The evaluation is conducted by calculating the Root Mean Square Error (RMSE) and the percentage of actual values within a 95% confidence interval on training and testing data. The results indicate that LSTM achieves the lowest RMSE, with values of 5.30E-05 on training data and 2.50E-05 on testing data, demonstrating high accuracy in capturing non-linear patterns and long-term fluctuations. GRU records the highest percentage of actual values within the confidence interval, at 90.32% for training data and 91.72% for testing data, reflecting superior consistency compared to other methods. Meanwhile, GARCH shows competitive performance but lacks robustness on testing data. CNN exhibits the lowest performance, with high RMSE and a low percentage of data within the confidence interval. Overall, GRU emerges as the best method, offering an optimal balance between predictive accuracy and consistency, making it a reliable tool for modeling exchange rate volatility in high-volatility scenarios. Consequently, GRU is utilized for forecasting exchange rate volatility for the next 30 days. These findings contribute to the selection of appropriate methods for modeling exchange rate volatility, particularly amidst global market uncertainty.

Bifurkasi pada Model Predator-Prey Diskret dengan Fungsi Respon Ratio-Depedent dan Pemanenan Suryanto, Agus; Krisnawati, Vira Hari; Lestari, Sri Puji; Matatula, Denis Andre; Fahrurrozy, Mohammad
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3450

This article discusses a predator-prey model with a ratio-dependent functional response and harvesting in both populations. The differential equation of predator-prey model is discretized using the Euler method. The dynamics of the obtained discrete time model are investigated by determining the fixed points as well as their stability properties, and bifurcation analysis. Bifurcation analysis shows that the discrete time model can experience bifurcation, both period-doubling bifurcation and Neimark-Sacker bifurcation, when the value of time-integration step passes a critical value. The analysis results have been confirmed by our numerical simulation results presented at the end of this article.

Dimensi Metrik pada Graf Bintang Kipas dan Graf Bunga Sepatu Khusniyatinna'im, Layinatu; Kusmayadi, Tri Tri Atmojo; Martini, Titin Sri
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3455

Let be a connected graph with set of vertices and set of edges . The distance from two distinct vertices , denoted by , is the length of the shortest path from and in . Let be an ordered subset of . For any vertex , the representation of vertex with respect to is defined as k-ordered pairs . The set is said to be the resolving set of if every two vertices differ then . The basis of is the resolving set of with the smallest cardinality. The cardinality of the base is defined as metric dimension, and is denoted by . This research aims to find the metric dimension of fan star graph and hibiscus graph. The research method in this research is a literature study. The result of this research are as follow the metric dimension of the fan star graph are for and and for dan , then the metric dimension of the hibiscus gaph are for and for .

Bilangan Kromatik Lokasi Graf Tentakel Putri, Azizah Riana; Sy, Syafrizal; Helmi, Monika Rianti
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3462

The locating-chromatic number of a graph was introduced by Chartrand et al. in 2002, which is a combined concept between the vertex coloring and partition dimension of a graph. The locating-chromatic number of a graph is a grouping of vertices on a graph based on color, which is called a color class, provided that each vertex on the graph has a different color code. Determining the locating-chromatic number of a graph is done by constructing the lower and upper bound of the locating-chromatic number of the graph. In this paper, we determine the locating-chromatic number of the tentacle graph, which is denoted by T_(k,m,n). Tentacle Graph is a graph constructed from a triangular book graph Bt_n whose common edge is amalgamated with C_k. Then two vertices in C_k that are adjacent to the vertex associated with the terminal edge are amalgamated with the star graphs S_(n_1) and S_(n_2). By determining the lower and upper bounds of the location chromatic number, it is obtained that the location chromatic number of Tentacle Graph is 4, m=1,n=2, n+1, for m>=1, n>= m + 2, and m + 2, for m > 1, n < m + 2.

Penjadwalan Kereta Bandara dan Commuter Line Yogyakarta Menggunakan Aljabar Max-Plus Pramesti, Nindya Yan; Putri, Angela Merici Olivia; Rudhito, Marcellinus Andy
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3463

Trains serve as a crucial mode of public transportation, significantly impacting people's mobility. Residents of Solo and Yogyakarta have experienced firsthand the benefits of trains for traveling between cities, whether using commuter or airport trains. However, the schedules for the YIA airport train, Adi-Soemarmo airport train, and Yogyakarta Commuter Line are not currently coordinated, as they are planned based solely on passenger demand. Synchronizing the departure times of these three train types is essential to ensure that trains are available when passengers need to transfer between different routes. This study aims to develop a network model for the departure schedules of the Yogyakarta Commuter Line, Yogyakarta International Airport (YIA) airport train, and Adi-Soemarmo airport train. It uses max-plus algebra to analyze the scheduling, culminating in the determination of eigenvalues and eigenvectors. The research employs literature review and Software Scilab. The findings revealed a maximum eigenvalue of (A) = 136 and an eigenvector in the form of a 16 1 real number matrix. Based on this maximum eigenvalue, a synchronized train schedule was created, with departures every 2 hours and 16 minutes, or 136 minutes.

Perbandingan Metode Euler - Estimasi Galat Neural Network dan Metode Runge Kutta Orde 4 dalam Menyelesaikan Persamaan Diferensial Biasa Linear Herdiana, Ratna; Alfiani, Clarine
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3467

Linear ordinary differential equations are a type of differential equation that is generally easy to solve analytically when the function on a partial integral has a simple form. However, when the function is a difficult function, it requires other methods such as numerical methods and methods adapted from neural networks because analytical methods can only be used when the problem has a simple geometric interpretation. This study involves the Euler method followed by error estimation using neural networks and the Runge-Kutta Orde-4 method as a comparison. The comparison was carried out by solving four equations which were then analyzed for the results and errors in each method based on the graphs generated and the MAPE criteria. The results of the study based on graphs show that the error generated by the method with error estimation using neural networks is more stable than the 4th Order Runge-Kutta method. In addition, based on the results of calculations with the MAPE criteria, the error estimation method using neural networks produces a very high level of accuracy in the category, while the 4th Order Runge-Kutta method produces a level of accuracy in two categories, namely the very high and reasonable categories

Comparative Analysis of Mathematical Models: A Case Study of Used Smartphone Price Depreciation Chandrawisesa, Muhammad Nezha Alfatah; Safitri, Annisa Rizky; Almuzakki, Muhammad Zaki; Tasmi, Tasmi
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3469

The price depression of the smartphone after it becomes used is one of the factors that consumers should consider when buying used smartphones. Therefore, accurate prediction of the price of used smartphones becomes a better insight into marketing strategies, and consumer purchasing decisions. The study aims to compare the performance of the Holt-Winters model damped, logistical decay, and exponential decay to predict the price depression of used smartphones. This research method uses historical data from some used smartphone prices as a basis for analysis. Comparisons between the three models were made to assess the performance of each in representing price depression behavior. Then, a statistical analysis was conducted to determine the most optimal model in predicting the price depression of used smartphones, the optimity of a model measured by the accuracy and speed of the computer performing the model execution. The accuracy measure in this study is the mean square error (MSE) value generated by a model with historical data alignment based on the ratio to the price when the smartphone has not been indicated as usable and the execution speed measure is the time it takes a computer to execute the model. The results show that the Holt-Winters damped model provides the most optimal predictive results compared to the exponential and decay models. This is demonstrated by the lower MSE average value twice as low as compared with the other two models, on the other hand, the holt-winters Damped has the weakness of requiring the longest average execution time of the three models with an average performance speed of 2.7 seconds, but the shortfall is not fatal because the predicted time period in this case is monthly so there is no urgency to advance the speed of seconds rather than accuracy.

Diffusion-Advection Reaction in Gierer-Meindhart System Trynita, Annisa Diva Putri; Sutrima, Sutrima
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3471

Gierer-Meinhardt system is a mathematical model commonly used to describe chemical and biological phenomena, specifically the interaction between two types of molecules: activator and inhibitor. Diffusion reactions are processes where chemical molecules move from areas of high concentration to areas of low concentration randomly. In this research, the Gierer Meinhardt system with advection components is considered. The mathematical model developed consists of partial differential equations (PDE) for two variables, namely the activator and the inhibitor, with the addition of an advection component that depends on the flow speed. Studies show that the presence of advection significantly affects the characteristics of the patterns formed. Advection reactions cause more regular and oriented patterns compared to patterns produced only by diffusion. This research uses theoretical analysis methods and literature studies to analyze the impact of advection-diffusion reactions on the Gierer Meinhardt system. In this research, it is concluded that the equilibrium point which was initially stable when becomes stable only when and .

Ketimpangan Pendapatan antara Wilayah Perkotaan dan Perdesaan di Indonesia tahun 2019-2023 Simbolon, Rika Lusiana; Sirait, Timbang
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3912

One of the biggest challenges in income inequality is the existence of income inequality between urban and rural areas, especially in developing countries. In 2019-2023, the average income of urban residents was 1.7 times higher than that of rural residents. The existence of income gaps between urban and rural areas can hinder equitable economic growth and worsen social inequality. Currently, household income is greatly influenced by the integration between the digital economy and the real economy. The development of the digital economy plays a role in increasing economic growth. However, its acceleration risks worsening social exclusion, inequality between groups, and wealth concentration. Therefore, this study aims to analyze the influence of the digital economy on income inequality between urban and rural areas in 33 provinces in Indonesia in 2019-2023 using a panel regression model. The results of measuring income inequality using the Theil L index show that the contribution of income inequality between urban and rural areas to national inequality has decreased in 2019-2023. The development of the digital economy in terms of infrastructure, business climate, research and innovation, and funding/investment has a significant influence in reducing income inequality between urban and rural areas. Meanwhile, in terms of human resources, it has a significant influence in increasing income inequality between urban and rural areas.

Analisis Kualitas Layanan Aplikasi Ruangguru dengan E-Servqual dan Net Promoter Score (NPS) Subchan, Wafa; Safirin, Moch. Tutuk
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.4364

Digital transformation in the education sector has led to an increase in the use of online learning applications such as Ruangguru. Ruangguru is an online learning platform, which offers various digital products to support the learning process and provide a more interactive learning experience. However, meeting customer satisfaction and gaining user loyalty are key challenges in digital service development. This study aims to analyze the service quality of the Ruangguru application using the e-servqual approach which has seven dimensions, efficiency, fulfillment, reliability, privacy, responsiveness, compensation, and contact, to identify areas of improvement needed, as well as the Net Promoter Score (NPS) method to determine customer loyalty in using the Ruangguru application. Data was collected through questionnaires to 100 respondents who use the Ruangguru application. The results show that there is a gap between customer perceptions and customer expectations with a negative value, which indicates that the Ruangguru application has not met user expectations. The NPS value obtained from the formula calculation is 21, which indicates the level of customer loyalty is within the loyal parameter.

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Departemen Matematika Fakultas Sains dan Analitika Data Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya 60111, Indonesia Phone: +62-31-5943354 Email: limits.matematika@its.ac.id

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Jawa timur

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Home Page

OAI Link

Editorial Team

Contact

Reviewer

Google Scholar

Contact Name Chairul Imron

Contact Email cha_imron15@its.ac.id

Phone +6285648721814

Journal Mail Official limits.matematika@its.ac.id

Editorial Address Departemen Matematika Fakultas Sains dan Analitika Data Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya 60111, Indonesia Phone: +62-31-5943354 Email: limits.matematika@its.ac.id

Location Kota surabaya, Jawa timur INDONESIA

Abstract

Abstract

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Abstract

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Abstract

Contact Name
Chairul Imron

Contact Email
cha_imron15@its.ac.id

Phone
+6285648721814

Journal Mail Official
limits.matematika@its.ac.id

Editorial Address
Departemen Matematika Fakultas Sains dan Analitika Data Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya 60111, Indonesia Phone: +62-31-5943354 Email: limits.matematika@its.ac.id

Location
Kota surabaya,

Jawa timur

INDONESIA