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All Journal Techno.Com: Jurnal Teknologi Informasi CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society Journal of Mathematical and Fundamental Sciences Journal of Engineering and Technological Sciences BAREKENG: Jurnal Ilmu Matematika dan Terapan Scientific Contributions Oil and Gas
Kuntjoro Adji Sidarto
Institut Teknologi Bandung
Astronomy Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Approximate Solutions of Linearized Delay Differential Equations Arising from a Microbial Fermentation Process Using the Matrix Lambert Function Agus Yodi Gunawan; Kasbawati Kasbawati; Kuntjoro Adji Sidarto
Journal of Mathematical and Fundamental Sciences Vol. 48 No. 1 (2016)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2016.48.1.3

Abstract

In this paper we present approximate solutions of linearized delay differential equations using the matrix Lambert function. The equations arise from a microbial fermentation process in a metabolic system. The delay term appears due to the existence of a rate-limiting step in the fermentation pathway. We find that approximate solutions can be written as a linear combination of the Lambert function solutions in all branches. Simulations are presented for three cases of the ratio of the rate of glucose supply to the maximum reaction rate of the enzyme that experienced delay. The simulations are worked out by taking the principal branch of the matrix Lambert function as the most dominant mode. Our present numerical results show that the zeroth mode approach is quite reliable compared to the results given by classical numerical simulations using the Runge-Kutta method.
CONSTRUCTION OF THE BINO-TRINOMIAL METHOD USING THE FUZZY SET APPROACH FOR OPTION PRICING Agustina, Fitriani; Sumarti, Novriana; Sidarto, Kuntjoro Adji
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1775.179-204

Abstract

An option is a financial instrument that investors often use for speculation or hedging purposes. Calculating the profit in the investment using options also considers its price, so the investor needs to know the proper value of the option's price or at least the range of these values. This paper aims to improve the Bino-Trinomial tree model for determining the price of a European call option with a volatility parameter in the form of a triangular Fuzzy number. The Bino-Trinomial tree model is a combination of the Binomial and Trinomial trees that aims to control the values of its branches. Due to the involvement of the Fuzzy number, the obtained value of the option price is in a range or interval, so the investor could use it appropriately in arranging investment strategies. In the proposed model, the Fuzzy volatility parameter is utilized to capture the uncertainty of the estimated volatility in the financial market which can fluctuate from time to time. This parameter is expected to provide reasonable ranges and appropriate Fuzzy membership functions for option pricing so that investors can expect different optimal values for different risk preferences. We also adjusted the formulation of the increase and decrease factors in the Fuzzy Binomial tree to model stock price movements. Using different values of the volatility's sensitivity level and the option period, the results of numerical simulations show that prices of European call options given by the market are always within the option price range of the proposed model's result. Likewise, the results of the defuzzification of options prices in our Fuzzy Bino-Trinomial tree model are not much different from the prices given by the market. This shows that the Fuzzy Bino-Trinomial tree model performs better in determining the price of European call options than the Fuzzy Binomial tree and Fuzzy Trinomial models.
A Fully Implicit Reservoir Simulation Using Physics Informed Neural Network Agus Wahyudi; Tutuka Ariadji; Taufan Marhaendrajana; Kuntjoro Adji Sidarto; Zuher Syihab
Scientific Contributions Oil and Gas Vol 48 No 3 (2025)
Publisher : Testing Center for Oil and Gas LEMIGAS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29017/scog.v48i3.1858

Abstract

The accuracy of simulation of multiphase flow in porous media is critical for reservoir management but is hindered by the nonlinear, coupled nature of governing equations and truncation errors in mesh-based numerical solvers. This study introduces a mesh-free, fully implicit Physics-Informed Neural Networks (PINN) framework for two-phase immiscible oil–water flow, where feedforward neural networks simultaneously approximate continuous pressure and saturation fields, embedding the governing PDEs, boundary, and initial conditions directly into the loss function. Three network topologies of single-row (N1), dual-row (N2), and branched-layer (NY) were tested across nine configurations which include variants of the networks. The novelty lies in the fully implicit PINN formulation of branched networks architectures with capability to reduce interference between pressure and saturation predictions. Benchmarking against the commercial simulator (Eclipse©) showed the NY achieved the best performance, with a mean squared error of less then 1.0×10-10. The N1 showed the ability to maintain stability at successive timesteps, while N2 models converged more slowly. The deep and narrow networks yielded higher accuracy but required almost double computation per iteration. Results demonstrate that even though with higher computational cost, the proposed PINN-based approach delivers high-fidelity solutions for complex reservoir problems without spatial meshing, offering a promising alternative to common numerical methods for both regular and irregular geometries.
Pricing Modified Barrier Options Using the Bino-Trinomial Tree Model: A Strategy for Loss Minimization Rima Aulia Rahayu; Fitriani Agustina; Kuntjoro Adji Sidarto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33239

Abstract

A particular exotic option that is widely traded in the global financial market is the barrier option. Barrier options are attractive because they have a limit that must be reached to activate the option. These limits may be utilized by investors as a point of reference to minimize potential losses. Accordingly, the researcher attempts to use the bino-trinomial tree model as a new approach to minimize losses. The purpose of this study is to analyze the bino-trinomial tree model to provide investors with more flexible hedging experience. The bino-trinomial tree model is obtained by combining the trinomial tree model at the first stage, then the binomial tree model at a further stage. This analysis was conducted by calculating the type of knock-out european call options. The results demonstrate that this model can effectively, accurately and flexibly manage the complex options required by modern investors, including multi-step single moving barrier options and single window barrier options.
ENHANCED GIANT TREVALLY OPTIMIZER FOR ENGINEERING DESIGN AND EPIDEMIOLOGICAL MODEL Ikhsan Rizqi Az-Zukruf As-Shidiq; E. Andry Dwi Kurniawan; Kuntjoro Adji Sidarto
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1229-1250

Abstract

Metaheuristic algorithms are widely used for solving complex optimization problems, but their performance often depends on the initialization strategy. This study proposes an enhanced Giant Trevally Optimizer (GTO) by introducing quasi-random Sobol sequences in the initialization phase, yielding the Sobol-initialized Giant Trevally Optimizer (SGTO). The algorithm was tested on forty benchmark functions, five engineering design problems, and an epidemiological model case study. Experimental results show that SGTO consistently outperforms the original GTO in terms of achieving optimal solutions, convergence, and its ability to maintain a consistent solution across multiple independent runs. Furthermore, the epidemiological case study demonstrates the adaptability of SGTO for tackling more complex real-world problems. This work is the first to adapt Sobol sequences for the GTO and apply it to an epidemiological model. These findings confirm that quasi-random initialization substantially improves exploration and exploitation, establishing SGTO as a versatile and reliable optimization tool.
ISLAMIC MORTGAGE FINANCING: DETERMINATION OF AN OPTIMAL NISBAH OF PROFIT-SHARING SCHEME UNDER MUSHARAKAH MUTANAQISAH CONTRACT Wulan Nurul Kamilah; Novriana Sumarti; Kuntjoro Adji Sidarto
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0841-0852

Abstract

In an Islamic investment using a profit-sharing scheme, one of the important issues to be determined is the optimal value of nisbah, so that all the parties are fairly treated. This study aims to determine the optimal constant nisbah for an Islamic home financing under musharakah mutanaqisah (MMQ) contract, to ensure a fair arrangement for both parties: the Islamic Bank (IB) and the customer. Under MMQ, the model combines partnership (Musharakah) and a leasing agreement, with gradual ownership transfer from the IB to the customers using an installment payment. For describing its dynamic, the customer’s income is assumed to follow the Geometric Brownian Motion (GMB), and the defined objective function is solved using the simulated data of payments of rental fee and ownership installment. Based on the simulation results, it will show that the middle value of a parameter of the defined objective function as a biased portion, with , is not always chosen. The objective function, which shows a parabolic plot trend, can be interpreted as a fair situation between the IB and the customer. With the selected α value, the maximum objective function value will be sought. The determined nisbah can inform policy decisions in Islamic financial institutions.
Co-Authors Aang Nuryaman Abu Rizal Agus Wahyudi Agus Yodi Gunawan Amoranto Trisnobudi Darmadi Darmadi Darmadi Darmadi Darmadi Darmadi Darmadi, Darmadi Delint Ira Setyoadi Delint Ira Setyoadi E. Andry Dwi Kurniawan Edy Soewono Fitriani agustina Ikhsan Rizqi Az-Zukruf As-Shidiq Kania, Adhe Kasbawati Kasbawati Kenny David Kenny David Lala Septem Riza Leksono Mucharam Moch Fandi Ansori Mucharam, Leksono Muhammad Syamsuddin Nancy Rohani Nancy Rohani Novriana Sumarti Novriana Sumarti Pudjo Sukarno Pudjo Sukarno Pudjo Sukarno Pudjo Sukarno R. Arman Widhymarmanto Rahmat Karim Rima Aulia Rahayu Suharsono Bantun Taufan Marhaendrajana Tutuka Ariadji Tutuka Ariadji Vina Fitriyani Mardiyyah Widhymarmanto, R. Arman Wulan Nurul Kamilah Yogi Wibisono Budhi Zuher Syihab