Perbandingan Metode Euler Dan Metode Runge-Kutta Orde 4 Pada Proses Pengisian Dan Pengosongan Kapasitor

Nurhamidah, Nurhamidah; Mabruroh, Faizatul; Putri, Jamiatul Khairunnisa; Latifah, Annisa Nur

doi:10.36706/jipf.v9i2.18531

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“…[12] membahas komparasi metode euler, modifikasi metode euler, serta runge kutta untuk menyelesaikan beberapa kasus nilai awal secara numerik. Sementara itu, perbandingan metode Euler dan metode Runge-Kutta dibahas pada kasus pemodelan yang merepresentasikan proses pengisian dan pengosongan kapasitor [13]. Selanjutnya, Rahayu, dkk., [14] melakukan analisis secara komparatif antara metode Euler dengan Jacobian pada kasus proyeksi pertumbuhan penduduk.…”

Section: Pendahuluanunclassified

Komparasi Skema Numerik Euler, Runge-Kutta dan Adam-Basforth-Moulton untuk Menyelesaikan Solusi Persamaan Osilator Harmonik

Resmawan,

Rosydah,

Handayani

2023

Euler J. Ilm. Mat. Sains dan Teknol.

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This article discusses the comparison of different numerical schemes to visualize the solution of 2nd-order differential equations. One-step methods such as the Euler method and the 4th-order Runge-Kutta method are combined with the 3rd-order Adam-Bashforth-Moulton method to solve the solution of 2nd-order differential equations. This combination of methods solves the Harmonic Oscillator equation, an 2nd-order differential equation widely applied in various oscillation contexts. The order of accuracy and order of approximation error are determined analytically. Finally, simulations are given with different steps for the three methods to confirm the behavior of the solution to the Harmonic Oscillator equation. The results show that the Euler method with the lowest order of accuracy has good accuracy at the beginning of the oscillation but not when time t is increased. The Runge-Kutta method, with the highest order of accuracy, shows excellent and consistent accuracy and solution stability, while the Adam-Bashforth-Moulton method, although it has a lower accuracy than the Runge-Kutta method of order 4, can be improved by choosing a one-step method with a high order of accuracy to approximate some of the required initial solutions. All three methods can provide approximation values with excellent accuracy and stability if a small step, h, is chosen, but this step can increase the time duration to display the solution. Thus, it is necessary to choose the right h according to the context of the equation and the method used to obtain accurate solutions with optimal time duration.

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Section: Pendahuluanunclassified