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NUGRAHANI, E. H.
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Mathematics

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SOLUSI NUMERIK PERSAMAAN BOLTZMANN NUGRAHANI, E. H.
MILANG Journal of Mathematics and Its Applications Vol. 2 No. 1 (2003): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.2.1.37-44

Abstract

Particle methods are well known tools to solve the kinetic Boltzmann equation numerically. The usual procedure of such method is the direct simulation Monte-Carlo, which directly simulate the collision between particles. The second method of interest is the stochastic weighted particle method, which is developed to improve the previous method. The main idea of the second method is to use random weight transfer between particles during collisions. In order to reduce the stochastic fluctuations, this method provides a way to increase the number of particles. But if the additional particles cannot be compensated in some natural way, then this number should be reduced. Several reduction procedures have been proposed. Some numerical results using both methods are presented. It is shown that the second method gives some better results in some ways.
CELLULAR AUTOMATA SIMULATION OF TRAFFIC LIGHT STRATEGIES IN OPTIMIZING THE TRAFFIC FLOW NUGRAHANI, E. H.; RAMDHANI, R.
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.4.2.13-20

Abstract

The behavior of traffic system controlled by traffic lights is presented under assumptions of city traffic on a single lane based on the optimal velocity model.  The effect of differrent traffic light control strategies on the traffic flow is discussed using three different strategies, i.e. the synchronized, green wave, and random offset strategies. The flow-density diagrams are analyzed using these strategies.   The numerical investigation is carried out using cellular automata model to get a better understanding of the microscopic behavior of the system under the three different traffic light strategies.
MODEL PERTUMBUHAN EKONOMI DUA DAERAH DAN SIMULASI EFEK PERUBAHAN PARAMETERNY TAUFIK, N. T.; NUGRAHANI, E. H.; BUDIARTI, R.
MILANG Journal of Mathematics and Its Applications Vol. 7 No. 1 (2008): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.7.1.47-57

Abstract

The traditional growth theory usually considers only the accumulation of conventional inputs of labor and capital as the primary variables responsible for the growth. It has been proven to be insufficient for explaining the complexity of modern economic growth. This thesis aims to study a two-region economic growth model proposed by Zhang (2005). This model explains the dynamics of economic system based on capital and knowledge accumulation. It also considers relationships between regional growth and regional trade patterns. Each region's production is similar to the standard one-sector growth model. Knowledge accumulation is assumed to be accomplished through learning by doing. Unfortunately, in obtaining the equilibrium solution of the model Zhang made some mistakes. Therefore, this thesis offers some corrections. The analysis done in this thesis includes obtaining equilibrium of the economic system and its feasibility conditions. Some results of simulation study show that knowledge improvement is more effective to increase equilibrium value of economic growth compared to improvement in investment or amenity level.
MODEL PERTUMBUHAN EKONOMI ANTAR KELOMPOK DAN SIMULASINYA HERLIANI, A. L.; NUGRAHANI, E. H.; LESMANA, D. C.
MILANG Journal of Mathematics and Its Applications Vol. 8 No. 1 (2009): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.8.1.67-79

Abstract

Domar’s economic growth model only considers capital as primary variable for production function. On the other hand, Solow’s economic growth model has added the labor as variable in the production function. The aim of this paper is to study distribution model of economic growth among groups in two regions proposed by Zhang (2005). This model considers human capital productivity as one of parameters of the production function. It has been shown that the dynamical system has a unique equilibrium. Therefore, the changes of human capital and propensity to save will influence total capital stocks and capital stocks in each group. Analytically, it is found that an increase in human capital and propensity to save will increase total capital stocks and capital stocks in each group.
MODEL PERDAGANGAN ANTAR NEGARA BERDASARKAN AKUMULASI MODAL DAYAT, D.; NUGRAHANI, E. H.; BUDIARTI, R.
MILANG Journal of Mathematics and Its Applications Vol. 8 No. 2 (2009): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.8.2.27-36

Abstract

Model perdagangan antarnegara dikembangkan untuk mengkaji kemungkinan terjadinya pola perdagangan antarnegara dengan perbedaan preferensi, fungsi produksi, dan perpindahan modal internasional secara sempurna. Konsumsi dan tabungan diturunkan dari optimasi fungsi utilitas. Ditunjukkan bagaimana perbedaan preferensi dan fungsi produksi dapat berpengaruh pada arah perdagangan dalam sistem dinamik. Hasil analisis disimpulkan bahwa pada saat ekuilibrium sistem dinamik memiliki solusi tunggal. Hasil simulasi menunjukkan bahwa peningkatan tingkat teknologi dari suatu negara berpengaruh pada peningkatan cadangan modal keseluruhan, cadangan modal dan tingkat produksi negaratersebut. Peningkatan tingkat kecenderungan untuk menabung suatu negara mengakibatkan peningkatan cadangan modal dan pengurangan penggunaan modal asing atau peningkatan pemberian modal kepada negara asing
OPSI BARRIER SAHAM TIPE UP-AND-OUT CALL DI BURSA EFEK INDONESIA SELEKY, J. S.; NUGRAHANI, E. H.; PURNABA, I G. P.
MILANG Journal of Mathematics and Its Applications Vol. 11 No. 1 (2012): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.11.1.1-10

Abstract

Kontrak opsi saham adalah efek yang memuat opsi call yang memberikan hak kepada pemegang opsi untuk membeli sejumlah tertentu dari sebuah instrumen yang menjadi dasar kontrak dalam jangka waktu dan harga tertentu. Model Black-Scholes adalah model kontinu untuk menentukan nilai dari opsi tipe Eropa. Sedangkan untuk menentukan nilai opsi tipe Amerika digunakan metode binomial tree. Dalam paper ini akan ditunjukkan bahwa nilai pendekatan numerik dari model diskret dengan metode binomial tree akan mendekati nilai dari model kontinu Black-Scholes. Hasil dari simulasi yang dilakukan sesuai dengan teori yang sudah dikembangkan, yaitu nilai dari opsi saham tipe up-and-out call Amerika Iebih murah dibandingkan dengan nilai dari opsi call regular tipe Amerika.
Co-Authors AYUDIAH, W. BUDIARTI, R. DAYAT, D. GARNADI, A. D. HANUM, F. HERLIANI, A. L. KAMILA, I. KURNIA, M. T. LESMANA, D. C. M. Ilyas, M. MAHMUD, S. L. MELIYANI, R. PURNABA, I G. P. PURWIANTI, T. PUTRA, Y. S. RAMDHANI, R. ROSMELY, R. SELEKY, J. S. SIANTURI, P. SUKANDAR, R. S. SUMARNO, H. SUSANTI, S. TAUFIK, N. T. YULIANY, E. YULIAWATI, L.