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All Journal Jurnal Matematika UNAND Journal of Multidisciplinary Applied Natural Science Transcendent Journal of Mathematics and Applications
Putra, Gusrian
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Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Economics, Econometrics & Finance Energy Environmental Science Immunology & microbiology Materials Science & Nanotechnology Mathematics Physics

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METODE TELESCOPING DECOMPOSITION METHOD PADA PERSAMAAN LOGISTIK WINDARTO-ERIDANI-PURWATI DALAM ORDE FRAKSIONAL Putra, Gusrian; Mardianto, Lutfi; Patra, Nugraha Catur Septian
Jurnal Matematika UNAND Vol 13, No 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.222-229.2024

Abstract

Model logistik Windarto-Eridani-Purwati (WEP) merupakan modifikasi model pertumbuhan logistik dan model monomolekuler yang digunakan untuk menggambarkan pertumbuhan organisme. Penelitian ini bertujuan mengkaji model logistik WEP dalam orde fraksional. Perbandingan dilakukan untuk mengetahui model dengan akurasi yang lebih baik. Metode yang digunakan untuk memperoleh solusi model logistik WEP dalam orde fraksional yaitu Telescoping Decomposition Method (TDM) dan metode Euler. Berdasarkan perhitungan yang telah dilakukan didapatkan model logistik WEP orde fraksional lebih baik dibandingkan model logistik WEP. Hal ini dikarenakan pada model logistik orde fraksional dapat dilakukan suatu pengaturan dalam menetapkan orde fraksionalnya sehingga model logistik WEP orde fraksional lebih fleksibel untuk menghampiri data yang empiris.
Method of multiple scales on Duffing oscillator equation and the existence of its limit cycle Putra, Gusrian; Supmawati, Meysi; Prasetyo, Bayu
Transcendent Journal of Mathematics and Applications Vol 2, No 2 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i2.34035

Abstract

The Duffing Oscillator equation is a second-order nonlinear differential equation that describes an oscillator with a cubic nonlinearity. In this paper, the Duffing equation involves damping factors, restoring forces, periodic force and its frequency, and nonlinearity constants. One of the perturbation techniques that can be used to determine the approximate solution of the Duffing oscillator equation is the method of Multiple Scales. Due to the existence of a sinusoidal periodic force in the equation, the Multiple Scales method produces a sinusoidal approximation as its solution. The solutions are also in a good agreement with the numerical results for small nonlinearity constants. The smaller the nonlinearity constant, the smaller the error obtained with the numerical results in comparison. The approximate solution also tends to be sinusoidal for small nonlinearity constants. Finally, the approximate solution obtained is able to predict the existence of a limit cycle in the Duffing Oscillator equation around the origin due to the existence of its particular solutions.
Numerical Solution of European Put Option for Black-Scholes Model Using Keller Box Method Mardianto, Lutfi; Putra, Gusrian; Pratama, Benediktus Ivan; Putri, Endah R. M.
Jurnal Matematika UNAND Vol. 13 No. 3 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.3.188-197.2024

Abstract

In this study, we propose to determine option pricing by using Black-Scholes model numerically. The Keller box method, a numerical method with a box-shaped implicit scheme, is chosen to solve the problem of pricing stock options, especially European-put option. This option pricing involves several parameters such as stock price volatility, risk-free interest rate and strike price. The numerical stability of the method is checked using Von Neumann stability before the simulation is conducted. The influence of interest rates, volatility, and strike price on the option price state that the higher the value of the interest rate parameter, the lower the option price value, while the greater the value of stock price volatility and strike price, the higher the option price.
METODE TELESCOPING DECOMPOSITION METHOD PADA PERSAMAAN LOGISTIK WINDARTO-ERIDANI-PURWATI DALAM ORDE FRAKSIONAL Putra, Gusrian; Mardianto, Lutfi; Patra, Nugraha Catur Septian
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.222-229.2024

Abstract

Model logistik Windarto-Eridani-Purwati (WEP) merupakan modifikasi model pertumbuhan logistik dan model monomolekuler yang digunakan untuk menggambarkan pertumbuhan organisme. Penelitian ini bertujuan mengkaji model logistik WEP dalam orde fraksional. Perbandingan dilakukan untuk mengetahui model dengan akurasi yang lebih baik. Metode yang digunakan untuk memperoleh solusi model logistik WEP dalam orde fraksional yaitu Telescoping Decomposition Method (TDM) dan metode Euler. Berdasarkan perhitungan yang telah dilakukan didapatkan model logistik WEP orde fraksional lebih baik dibandingkan model logistik WEP. Hal ini dikarenakan pada model logistik orde fraksional dapat dilakukan suatu pengaturan dalam menetapkan orde fraksionalnya sehingga model logistik WEP orde fraksional lebih fleksibel untuk menghampiri data yang empiris.
Optimization of Star Pomfret Feed Production as a Linear Programming Problem Using a Hybrid Wolfe-Differential Evolution Algorithm Febrianti, Werry; Putra, Gusrian; Syari, Chalida; Abdallah, M Naif
Journal of Multidisciplinary Applied Natural Science Vol. 5 No. 2 (2025): Journal of Multidisciplinary Applied Natural Science
Publisher : Pandawa Institute

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47352/jmans.2774-3047.255

Abstract

Star pomfret (Trachinotus blochii) is one of the most sought-after types of marine fish in Indonesia. The production of feed for star pomfret fish is an important factor because it is related to their survival and ability to grow well.  Therefore, formulating the feed formulation for star pomfret (Trachinotus blochii) is very important to minimize feed production costs and ensure the nutritional adequacy of the fish. Therefore, we change the feed for star pomfret fish as a linear programming (LP) problem and solve it using the Hybrid Differential Evolution-Wolfe Algorithm (HWDEA).  HWDEA combines the Wolfe method, which efficiently transforms constraints into a system of linear equations, with the use of the Differential Evolution Algorithm (DEA) to find a global optimization solution, which is a solution that is not trapped in a local minimum.  We improve accuracy and efficiency by using HWDEA to find the optimal solution for this fish feed production. Our HWDEA can also overcome the limitations of traditional methods such as the simplex algorithm.  Thus, we can show that HWDEA successfully reduced feed production costs from 12,353 IDR to 9,035 IDR per kg while maintaining nutritional balance.  We can conclude that the HWDEA method successfully adapted to price fluctuations and raw material availability, allowing it to produce an optimal raw material composition in feed production.  Therefore, HWDEA can be used as an efficient tool to provide significant cost savings for supporting sustainable and profitable fish farming.
Co-Authors Abdallah, M Naif Bayu Prasetyo, Bayu Chalida Syari Febrianti, Werry Mardianto, Lutfi Patra, Nugraha Catur Septian Pratama, Benediktus Ivan Putri, Endah R. M. Supmawati, Meysi