Solusi Numerik pada Persamaan Korteweg-De Vries Equation menggunakan Metode Beda Hingga

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that has a key role in wave physics and many other disciplines. In this article, we develop numerical solutions of the KdV equation using the finite difference method with the Crank-Nicolson scheme. We explain the basic theory behind the KdV equation and the finite difference method, and outline the implementation of the Crank-Nicolson scheme in this context. We also give an overview of the space and time discretization and initial conditions used in the simulation. The results of these simulations are presented through graphical visualizations, which allow us to understand how the KdV solution evolves over time. Through analysis of the results, we explore the behavior of the solutions and perform comparisons with exact solutions in certain cases. Our conclusion summarizes our findings and discusses the advantages and limitations of the method used. We also provide suggestions for future research in this area.Persamaan Korteweg-de Vries (KdV) adalah persamaan diferensial parsial nonlinear yang memiliki peran kunci dalam fisika gelombang dan banyak disiplin ilmu lainnya. Dalam artikel ini, kami mengembangkan solusi numerik persamaan KdV menggunakan metode beda hingga dengan skema Crank-Nicolson. Kami menjelaskan teori dasar di balik persamaan KdV dan metode beda hingga, serta menguraikan implementasi skema Crank-Nicolson dalam konteks ini. Kami juga memberikan gambaran tentang diskritisasi ruang dan waktu serta kondisi awal yang digunakan dalam simulasi. Hasil dari simulasi ini dipresentasikan melalui visualisasi grafis, yang memungkinkan kita untuk memahami bagaimana solusi KdV berkembang seiring berjalannya waktu. Melalui analisis hasil, kami mengeksplorasi perilaku solusi dan melakukan perbandingan dengan solusi eksak dalam kasus tertentu. Kesimpulan kami merangkum temuan kami dan mendiskusikan keuntungan dan keterbatasan metode yang digunakan. Kami juga memberikan saran untuk penelitian selanjutnya dalam bidang ini. Kata kunci: Persamaan KdV, Soliton, Metode bedahingga, skema Crank-nicolso

Solution of The Duffing Equation Using Exponential Time Differencing Method

To describe the spring stiffening effect that occurs in physics and engineering problems, Georg Duffing added the cubic stiffness term to the linear harmonic oscillator equation and is now known as the Duffing oscillator. Despite its simplicity, its dynamic behavior is very diverse. In this research, the Exponential Time Difference method is introduced to solve the Duffing oscillator numerically. To formulate the ETD method, we were using the integration factors. It is a function which, when multiplied by an ordinary differential equation, produces a differential equation that can be integrated. This method is an effective numerical method for solving complex differential equations, especially equations that have strong non-linearity The ETD method delivers highly accurate numerical solutions for the Duffing oscillator, with minimal discrepancy from the analytical results. Through parameter variation, the ETD method's applicability extends to diverse Duffing oscillator configurations

Forecasting Coffee Exports to the United States Using the Holt-Winters Exponential Method

A study was conducted to estimate coffee exports to the United States using the Holt-Winters Exponential method. The aim of this research is to project coffee export activity over the next four periods. Data on coffee exports to the United States from 2000 to 2022 was obtained from the Indonesian Central Bureau of Statistics and used as a research object. The range of values used in this study is between 0.1 and 0.5 for α, between 0.1 and 0.5 for β, and between 0.1 and 0.9 for ϒ. The results of this research state that it is estimated that in 2023, Indonesia will export coffee to the United States amounting to 61,332.60 tons, in 2024 amounting to 60,661.50 tons, in 2025 amounting to 61,563.27 tons, and in 2026 amounting to 60,196.50 tonsSebuah studi telah dilakukan untuk meramalkan ekspor kopi ke Amerika Serikat menggunakan metode Holt-Winters Exponential. Tujuan dari penelitian ini adalah untuk memproyeksikan aktivitas ekspor kopi selama empat periode ke depan. Data ekspor kopi ke Amerika Serikat dari tahun 2000 hingga 2022 diperoleh dari Badan Pusat Statistik Indonesia dan dijadikan sebagai objek penelitian. Rentang nilai yang digunakan dalam studi ini adalah antara 0,1 dan 0,5 untuk α, antara 0,1 dan 0,5 untuk β, dan antara 0,1 dan 0,9 untuk ϒ. Hasil dari penelitian ini menyatakan bahwa diperkirakan pada tahun 2023, Indonesia akan mengekspor kopi ke Amerika Serikat sebesar 61.332,60 ton, pada tahun 2024 sebesar 60.661,50 ton, pada tahun 2025 sebesar 61.563,27 ton, dan pada tahun 2026 sebesar 60.196,50 ton

Forecasting Non-Metal and Rock Mineral (MBLB) Tax Revenue Using the Fuzzy Time Series Markov Chain Method in East Lombok Regency

Indonesia is one of the countries that is included in a developing countries. Therefore, the Indonesian Goverment is trying to carry out various developments in various regions. Regional development is one of the Indonesian government’s ways of achieving national goals. In carrying out regional development, of course funds are needed as the main source to support the achievement of national development. The main source of funds obtained by the Government comes from Regional Oroginal Income. One source of Regional Oroginal Income is tax. There are various types of taxes managed by the government in East Lombok Regency. One of them is the Non-Metal Minerals and Rocks, which is a tax on the extraction of non-metallic minerals and rock Tax, which is a tax on the extraction of of non-metallic minerals and rocks from natural sources within or on the surface of the earth for use. This Non-Metal and Rock Mineral tax provides quite large revenues for East Lombok district regional taxes. Non-Metal and Rock Mineral tax income is often not constant, meaning that there is an increases and there is a decreases in the amount of income. For this reason, it is necessary to forecast Non-Metal and Rock Mineral tax revenue to predict income in the future. The method used in this study is the FTS Markov Chain order 1 and order 2. Based on the MAPE indicator, the results of forecasting using the FTS Markov Chain method of order 1 amounted to Rp. 1.117.069.497 with an accuracy of 48,55% with a just good forecasting classification. While the results of forecasting using the FTS Markov Chain method of order 2 amounted to Rp.1.761.652.173 with an accuracy of 39,12% with a just good forecasting classification. If seen from the MAPE value obtained, the forecasting results using the 2nd order FTS Markov Chain are more accurate than using the 1st order Markov Chain FTS method

Pemodelan Tingkat Pengangguran Terbuka di Indonesia Menggunakan Analisis Regresi Data Panel

Indonesia has entered the peak of the demographic bonus which can provide positive and negative impacts for various fields. One of them is in the economic field, namely the increasing number of productive population who are unabsorbed in the world of work and is referred to as an open unemployment. This research was conducted to build a model and to analyze the Open Unemployment Rate, Economic Growth, Provincial Minimum Wage, Level of education, Population growth, Labor Force Participation Rate, Employment, Human Development Index, Poor Residents, Illiterate Population, Average Length of School, Domestic Investment, Foreign Investment, and School Participation Rate, that influence the open unemployment rate in Indonesia using panel data regression analysis with data 2015-2021 from 34 provinces. A fixed effect model with different intercept values for every participant is the best panel data regression model (Fixed Effect Model) that could be found. Based on simultaneously research, it was discovered that every component of the model significantly effect the open unemployment rate. Partially, it was discovered that the following factors significantly effect the open unemployment rate in Indonesia: Employment, Labor Force Participation Rate, Economic Growth, Population Growth, Human Development Index, Poor Population, and Average years of Schooling.Indonesia telah memasuki puncak bonus demografi yang dapat memberikan dampak positif maupun dampak negatif terhadap berbagai bidang. Salah satunya dalam bidang ekonomi yakni semakin banyak populasi penduduk usia produktif yang tidak terserap dalam dunia kerja dan disebut sebagai pengangguran terbuka. Penelitian ini dilakukan untuk membangun model dan menganalisis faktor-faktor yang mempengaruhi tingkat pengangguran terbuka di Indonesia menggunakan analisis regresi data panel. Model regresi data panel terbaik yang diperoleh yakni model  pengaruh tetap dengan nilai intersep pada setiap individu berbeda (Fixed Effect Model). Berdasarkan penelitian diperoleh faktor-faktor yang signifikan mempengaruhi Tingkat Pengangguran Terbuka (TPT) di Indonesia yakni Pertumbuhan Ekonomi (), Pertumbuhan Penduduk (), Tingkat Partisipasi Angkatan Kerja (), Penyerapan Tenaga Kerja (), Indeks Pembangunan Manusia (), Penduduk Miskin (), dan Rata-rata Lama Sekolah () dengan koefisien determinasi () sebesar 44,81%

Analisis Dinamik Model Predator-prey dengan Perilaku Anti Predator serta Efek Allee pada Prey

We explore a predator-prey model that incorporates both anti-predator behavior by the prey and the Allee effect, where population growth declines at low densities. Four equilibrium points emerge: extinction for both species (E0), two predator extinction points (E1 and E2), and one coexistence point for both populations (E3). While the stability of E0, E2, and E3 depends on the given parameters, E1 is always unstable. We then verified this analysis through numerical simulations using Runge-Kutta method in Python.Kami mempelajari model predator-prey dengan perilaku anti-predator dan efek Allee pada prey. Efek Allee merupakan fenomena ekologi yang menggambarkan penurunan pertumbuhan populasi karena berkurangnya kepadatan suatu populasi spesies,  sedangkan perilaku anti predator adalah perilaku prey untuk melindungi diri dari predator. Kami menemukan 4 titik kesetimbangan, yaitu titik kepunahan kedua spesies , dua titik kepunahan predator  dan ) dan satu titik koeksistensi kedua spesies . Kestabilan  dan  tergantung dari parameter yang diberikan, sedangkan titik  selalu tidak stabil. Selanjutnya kami melakukan simulasi numerik dengan metode Runge-Kutta menggunakan bahasa pemrograman Python untuk mengkonfirmasi analisis model secara grafis

The ARIMA-GARCH Method in Case Study Forecasting the Daily Stock Price Index of PT. Jasa Marga (Persero)

PT Jasa Marga is a large company in Indonesia that develop and operation the toll roads and is known as one of the blue chip companies with LQ45 shares. However, share prices have high volatility or rise and fall quickly so their value is always changing. Therefore, forecasting is needed to predict the share price of PT Jasa Marga in the future in order to know the movement of its share price. The Autoregressive Integrated Moving Average (ARIMA) method is a method that can predict data with high volatility, but has the disadvantage of residuals containing heteroscedasticity. So, the addition of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model was carried out to overcome the heteroscedasticity problem that was initially caused by the ARIMA model so it could predict data with high volatility more optimally. Therefore, this research applies the ARIMA-GARCH method to find the best model for forecasting the daily share price index of PT Jasa Marga. The data used comes from the daily closing stock price index of PT Jasa Marga (Persero) for the period January 2015 to May 2023. The measurement of forecasting accuracy uses the Mean Absolute Percentage Error (MAPE). The forecasting results show that the best model uses ARIMA (2,1,1) - GARCH (1,3) with a MAPE value of 6.825728%, which indicates very good forecasting results because the MAPE value is <10%.PT Jasa Marga merupakan perusahaan besar di Indonesia yang berperan dalam pengembangan dan pengoperasian jalan tol yang dikenal sebagai salah satu perusahaan blue chip dengan saham LQ45. Namun, harga sahamnya memiliki volatilitas tinggi atau naik dan turun dengan cepat sehingga nilainya selalu berubah-ubah. Oleh karena itu, diperlukan adanya peramalan guna memprediksi harga saham PT Jasa Marga di masa yang akan datang guna mengetahui pergerakan harga sahamnya. Metode Autoregressive Integrated Moving Average (ARIMA) merupakan salah satu metode yang dapat meramalkan data dengan volatilitas tinggi, namun memiliki kekurangan pada residual yang mengandung heteroskedastisitas. Sehingga, dilakukan penambahan model Generalized Autoregressive Conditional Heteroskedasticity (GARCH) guna mengatasi masalah heteroskedastisitas yang awalnya, ditimbulkan model ARIMA sehingga dapat meramalkan data dengan volatilitas tinggi secara lebih optimal. Oleh karena itu, penelitian ini menerapkan metode ARIMA-GARCH guna menemukan model terbaik untuk meramalkan indeks harga saham harian PT Jasa Marga. Data yang digunakan berasal dari indeks penutupan harga saham harian PT Jasa Marga (Persero) periode Januari 2015 hingga Mei 2023. Pengukuran ketepatan peramalan menggunakan Mean Absolute Percentage Error (MAPE). Hasil peramalan menunjukkan model terbaik menggunakan ARIMA (2,1,1) - GARCH (1,3) dengan nilai MAPE sebesar 6,825728% yang mengindikasikan hasil peramalan sangat baik karena nilai MAPE < 10%

Modeling of the Spread of Malaria in the Bangka Belitung Islands Province Using the SEIR Method

Malaria is an infectious disease caused by plasmodium through the bite of the Anopheles sp. female mosquito. (Roach, 2012). Malaria disease which hit the Bangka Belitung Islands Province in 2005 experienced a spike, reaching 36,901 people out of 981,573 residents and claimed the lives of 12 local residents. In 2011, the Bangka Belitung Islands Province was declared an endemic area for malaria. This research aims to model and interpret the spread of malaria using the SEIR model and predict the spread of malaria using parameter estimates. The steps in analyzing the SEIR model on the spread of malaria are making assumptions, forming a SEIR model, determining the equilibrium point and analyzing the stability of the equilibrium point, determining the basic reproduction number, and carrying out a simulation of the SEIR model that has been obtained. The SEIR model is classified into 4 classes, namely Susceptible (susceptible individuals), Exposed (individuals who have symptoms), Infected (infected individuals), and Recovered (recovered individuals). The data used in this research is data on the number of Susceptible, Exposed, Infected, and Recovered malaria cases in 2022 obtained from the Bangka Belitung Islands Provincial Health Service. The SEIR mathematical model is used to calculate the equilibrium point and basic reproduction number. Based on the SEIR model simulation results, it was found that the susceptible population decreased from the 0th month to the 48th month. As for the exposed population, there were 9,623 people in month 0, but in this condition the population decreased drastically per month. Furthermore, for the infected population there were 129 people in month 0, but in this condition the number of infected decreased drastically per month along with the decrease in the exposed population. For individuals who recovered, there was a increase from the 0th month to the 48th month.Malaria is an infectious disease caused by plasmodium through the bite of the Anopheles sp mosquito. female (Roach, 2012). Malaria disease which hit the Bangka Belitung Islands Province in 2005 experienced a spike, reaching 36,901 people out of 981,573 residents and claimed the lives of 12 local residents. In 2011, the Bangka Belitung Islands Province was declared an endemic area for malaria. This research aims to model and interpret the spread of malaria using the SEIR model and predict the spread of malaria using parameter estimates. The steps in analyzing the SEIR model on the spread of malaria are making assumptions, forming a SEIR model, determining the equilibrium point and analyzing the stability of the equilibrium point, determining the basic reproduction number, and carrying out a simulation of the SEIR model that has been obtained. The SEIR model is classified into 4 classes, namely Susceptible (susceptible individuals), Exposed (individuals who have symptoms), Infected (infected individuals), and Recovered (recovered individuals). The data used in this research is data on the number of Susceptible, Exposed, Infected and Recovered malaria cases in 2022 obtained from the Bangka Belitung Islands Provincial Health Service. The SEIR mathematical model is used to calculate the equilibrium point and basic reproduction number. Based on the SEIR model simulation results, it was found that the susceptible population decreased from the 0th month to the 48th month. As for the exposed population, there were 9,623 people in month 0, but in this condition the population decreased drastically per month. Furthermore, for the infected population there were 129 people in month 0, but in this condition the number of infected decreased drastically per month along with the decrease in the exposed population. For individuals who recovered, there was a decrease from the 0th month to the 48th month

Negative Binomial and Generalized Poisson Regression Model for Death Due to Dengue Hemorrhagic Fever Data

Data on the number of deaths due to Dengue Fever in statistics is count data often approximated by a Poisson distribution. However, if overdispersion occurs, Poisson regression is no longer sufficient, so the Negative Binomial and Generalized Poisson Regression approaches are used. From the two models, the best model was chosen based on the smallest AIC value, 66.50, namely the Negative Binomial Regression model. From this model, factors that have a significant effect are determined based on the p-value, and the factor ratio of health facilities per 100,000 population  is obtained

Optimization of water flow on Regency Municipality Waterworks-network of Jonggat Central Lombok Regency using Ford Fulkerson Algorithm and Dinic Algorithm

Clean water is essential for humans which must be fulfilled for humans survival. The population in Jonggat, Central Lombok, increases from year to year which causes the using of clean water get an increase too. The necessity of rising clean water is not in line with the availability of water in nature, therefore the PDAM (Regency Municipality Waterworks) manages existing water resource. Then, it will be distributed to consumers. The purpose of this research is to determine the optimal solution in the distribution of clean water in Jonggat using Ford Fulkerson algorithm and Dinic algorithm. Both Ford Fulkerson algorithm and Dinic algorithm are methods used to calculate the maximum flow in a network. Based on the results of research using Python software on the Ford Fulkerson algorithm, the maximum current is 133 liters/second, while using the Dinic algorithm, the maximum current is 133.49 liters/second. Meanwhile, the average water flow is delivered by PDAM is 95 liters/second. It means, it can be added the amount of flow in the clean water distribution pipe by the PDAM. It’s for facilitating the flow of water that reaches consumers with the addition of a flow that cannot exceed 133.49 liters/second. Keywords:  Network flow, Maximum flow, Ford Fulkerson algorithm, Dinic algorith