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All Journal Limits: Journal of Mathematics and Its Applications International Journal of Computing Science and Applied Mathematics-IJCSAM
Lukman Hanafi
Department Of Mathematics, Institut Teknologi Sepuluh Nopember
Computer Science & IT Mathematics

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The Effect of Collector in Solar Still for Water Productivity Using Runge-Kutta Method Mardlijah Mardlijah; Achmad Fatoni; Lukman Hanafi
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 1 No. 1 (2015)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Solar still is a renewable energy technology. It can reduce crisis of clean and healthy water in some countries. Solar still produces clean and healthy water using the sunlight, but the result of distillate water is not so much. Hence the need for modifications with the addition of collector can increase the yield of distillate water. Mathematical model of solar still with collector is in the form of system of differential equations. It can be solved numerically using Runge-Kutta method. From the simulation, we conclude that the collector increases the amount of distillate water in the solar still.
Design of Monkeypox Virus Spread Control in Humans Using Pontryagin Minimum Principle Lukman Hanafi; Mardlijah Mardlijah; Daryono Budi Utomo; Suhud Wahyudi; Alya Nur Sha-brina
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 10 No. 2 (2024)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v10i2.4582

Abstract

Monkeypox is a contagious disease caused by a virus. In Africa, monkeypox results in death in 1 out of 10 infected individuals. The Food and Drug Administration in the United States recommends vaccination as a preventive measure against monkeypox virus. If infected, the World Health Organization (WHO) advises quarantine to prevent further transmission to others. This research develops a mathematical model known as SIR (Susceptible-Infected-Recovered) for the spread of monkeypox virus, incorporating vaccination and quarantine as control measures. The SIR model utilized is based on an existing model and follows the conditions of monkeypox spread in Nigeria, represented as a system of nonlinear differential equations. Optimal control is determined using the Pontryagin Minimum Principle and simulated using the fourth-order forward-backward sweep Runge-Kutta method to assess the level of monkeypox infection before and after implementing control measures. Based on the simulation results, it is concluded that the application of control measures can reduce the population of infected monkeys by 70% and infected humans by 59%.
On The Lagrange Interpolation of Fibonacci Sequence Muhammad Syifa'ul Mufid; Tahiyatul Asfihani; Lukman Hanafi
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 2 No. 3 (2016)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Fibonacci sequence is one of the most common sequences in mathematics. It was first introduced by Leonardo Pisa in his book Liber Abaci (1202). From the first n + 1 terms of Fibonacci sequence, a polynomial of degree at most n can be constructed using Lagrange interpolation. In this paper, we show that this Fibonacci Lagrange Interpolation Polynomial (FLIP) can be obtained both recursively and implicitly.
Construction of Cone 2-Norm Associated with S-Cone Inner Product Sadjidon Sadjidon; Mahmud Yunus; Sunarsini Sunarsini; Lukman Hanafi
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 9 No. 2 (2023)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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PENYELESAIAN NUMERIK UNTUK MENENTUKAN NILAI OPTIMAL PADA AMERICAN OPTION DENGAN METODE BEDA HINGGA FULLY IMPLISIT DAN CRANK-NICOLSON Lukman Hanafi; Endah Rohmati M.P.; G. M. Puspita
Limits: Journal of Mathematics and Its Applications Vol. 7 No. 2 (2010): Limits: Journal of Mathematics and Its Applications Volume 7 Nomor 2 Edisi Nove
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Option adalah sebuah kontrak keuangan yang memberikan hak kepada pemiliknya untuk membeli atau menjual sejumlah aset dasar dalam jangka waktu tertentu sesuai dengan harga yang disepakati pada saat penandatanganan kontrak option. American option sifatnya dapat diexercise sewaktu-waktu mulai dari penandatanganan kontrak sampai jatuh tempo. Melakukan exercise pada saat optimal adalah stategi yang dilakukan holder untuk mendapatkan keuntungan yang maksimal, namun waktu yang tepat untuk mendapatkan hasil yang optimal tersebut belum diketahui (free boundary-value problem). Penentuan harga optimal American option berdasarkan free boundary-value problem dilakukan pendiskritan persamaan Black-Scholes menggunakan metode Beda Hingga Fully Implisit dan Crank-Nicolson. Selanjutnya, kedua penyelesaian tersebut dibandingkan didapat bahwa Metode Beda Hingga Crank-Nicolson lebih baik berdasarkan kestabilan, konvergensi, dan akurasi.
Co-Authors Achmad Fatoni Alya Nur Sha-brina Daryono Budi Utomo Endah Rohmati M.P. G. M. Puspita Mardlijah - Muhammad Syifa'ul Mufid Muhammad Syifa'ul Mufid Sadjidon Sadjidon Suhud Wahyudi Sunarsini Sunarsini Tahiyatul Asfihani Tahiyatul Asfihani Yunus, Mahmud