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All Journal Limits: Journal of Mathematics and Its Applications International Journal of Computing Science and Applied Mathematics-IJCSAM
Tahiyatul Asfihani
Institut Teknologi Sepuluh Nopember
Computer Science & IT Mathematics

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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.
ANALISIS MODEL LINTASAN NANOPARTIKEL MAGNET PADA PEMBULUH DARAH DI DALAM MEDAN MAGNET DENGAN METODE RUNGE KUTTA ORDE KE-EMPAT Tahiyatul Asfihani; Hesti Hastuti; Chairul Imron
Limits: Journal of Mathematics and Its Applications Vol. 13 No. 1 (2016): Limits: Journal of Mathematics and Its Applications Volume 13 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Nanopartikel magnetik memiliki peran penting dalam dunia kedokteran modern yaitu sebagai obat yang ditargetkan oleh magnet. Obat yang ditargetkan oleh magnet tersebut disuntikan kedalam tubuh kemudian akan dibawa oleh darah mengalir ke seluruh tubuh. Untuk memperoleh hasil yang lebih optimal, diperlukan suatu model lintasan nanopartikel magnet didalam embuluh darah. Sistem tersebut dibantu dengan medan magnet yang diposisikan diluar tubuh. Dengan menggunakan metode Runge-kutta, diperoleh jarak antara pusat pembuluh darah dengan pusat medan magnet yang lebih tepat adalah 0.025 m dimana posisi lintasannya menuju kearah pusat medan magnet yaitu nol (z/Rm=0).
Disturbance Estimation for Unmanned Surface Vehicles using a Nonlinear Disturbance Observer Emilta Friska Juniar; Tahiyatul Asfihani
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 12 No. 1 (2026)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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An Unmanned Surface Vehicle (USV) is a maritime transportation system designed to operate autonomously. However, in complex marine environments, the vessel is subjected to external disturbances such as wind, ocean currents, and waves that can affect the stability and robustness of its motion control system. This study aims to estimate these disturbances in real time using a Nonlinear Disturbance Observer (NDO) and to utilize the estimated disturbances to update the predictive model in a Disturbance Compensating–Nonlinear Model Predictive Control (DC-NMPC) framework. The estimation considers two types of disturbances: constant disturbances representing steady wind and current forces, and periodic disturbances representing wave effects modeled as sinusoidal functions. These disturbances affect the sway velocity (v) and yaw velocity (r) of the vessel. Simulation results show that the NDO is capable of reconstructing the actual disturbances with bounded and consistent estimation errors. This is indicated by RMSE values of 0.0070 for d1 and 0.0605 for d2 under the tested disturbance scenario. The estimation performance remains consistent under variations of the observer gain matrix, indicating observer stability. Increasing the gain improves the estimation response speed but slightly increases the error, revealing a trade-off between responsiveness and estimation accuracy. Furthermore, the observer is able to track time-varying sinusoidal disturbances, demonstrating robustness against dynamic environmental disturbances. These results indicate thatNDO-based disturbance estimation can enhance the robustness of USV motion control under environmental disturbances.
Co-Authors Chairul Imron, Chairul Emilta Friska Juniar Hesti Hastuti Lukman Hanafi Muhammad Syifa'ul Mufid