Simulasi Numerik Model Matematika Vibrasi Dawai Flying Fox Menggunakan Metode Adams-Bashforth-Moulton

Abstract

This study discusses numerical simulation using the Adams-Bashforth-Moulton (ABM) method of order 4 in the flying fox string mathematical model which is in the form of ordinary differential equations depending on time, consisting of two equations, namely the equation of the flying fox string y(t) and the angular equation of the flying fox string θ(t). This mathematical model is a model that has been constructed by Kusumastuti, et al (2017) and has been validated by comparing analytical solutions to its numerical solutions by Sari (2018). The analysis of the behavior of the Kusumastuti 2017 model conducted by Makfiroh (2020) shows that the phase portrait graph is in the form of a spiral with eigenvectors pointing towards the equilibrium point so that the mathematical model of the flying fox string vibration can be concluded as a valid mathematical model that is close to the actual situation. This study attempts to determine the numerical simulation of the deflection of the flying fox string y(t) and the numerical simulation of the angle of the flying fox string θ(t). The Runge-Kutta method of order 4 was used to generate 3 initial values for order 4 ABM. Next, a comparison of the y(t) and θ(t) solution graphs of order 4 ABM with the solution graph with Runge-Kutta of order 4 was performed in Sari 2018. The first simulation was carried out when h=1, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 fluctuated in the range of [0,0.09] with almost the same graphic profile, and the difference in the value of θ(t) ABM of order 4, and Runge-Kuta order 4 which is quite large with different graphic profiles. The second simulation was carried out when h=0.01, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 was fluctuating which also ranged from [0.0.09] with the same graphic profile, and the difference in the values of θ(t) ABM of order 4 and Runge -Kutta order 4 fluctuates in the range of [0,1] with the same graphic profile. So concluded that when h=0.01 comparison of ABM of order 4 and Runge-Kutta of order 4 is the best for displaying the graph profiles of y(t) and θ(t). Further research can explore numerical solutions using other methods.