# Metode Runge-Kutta Orde 4 Dalam Penyelesaian Persamaan Gelombang 1D Syarat Batas Dirichlet

• Yenci Brika Enkekes Institut Teknologi Sumatera
• Lutfi Mardianto Program Studi Matematika Institut Teknologi Sumatera, Lampung Selatan, 35365, Indonesia

### Abstract

The problem studied in this study was the movement of deviations in the equation of 1D waves on the rope given the initial deviation value. In this study, the equation of 1D waves with dirichlet boundary problems will be solved analytically using variable and numerical separation using the runge-kutta method approach of order 4. This research begins with examining equation models, solving analytical solutions, applying schemes to the final results of simulations. The decrease in equation model fissile is done by reviewing the working force on a piece of rope, solving an analytical solution with a variable separation method, and numerical completion resulting in the best simulation result with parameter c= 0.5 with time steps ∆x= 0.01 and time interval of 0 ≤ t≤ 1 resulting in a numerical approach close to its analytical solution up to t= 1 s  and the influence of parameter c on the movement of wave deviations resulted in that the influence of parameter c affects the magnitude of the deviation of the wave, so the greater the value of parameter c, the smaller deviation of the wave and the faster the speed of the direction. Thus, it can be concluded that the runge-kutta method of order 4 in this study can be said to be one of the numerical approaches of the problem of 1D wave equations with dirichlet boundaries.

### References

 S. M. Hemmingsen, Soft Science. Saskatoon: University of Saskatchewan Press, 1997.
 Ross, S.L. (2004). Differential Equation. New York: John Wiley & Sons
 Resnick, Halliday. (1985). Physics, 3^rdEdition ( Fisika Dasar 1 Edisi Ketiga).
 Harijono Djojodiharjo Dr. Ir., (2000). Metode Numerik. Penerbit Erlangga-Jakarta
 Darmawijoyo, (2011). Persamaan Diferensial Biasa: Suatu Pengatar. Jakarta:Erlangga
 Wiryanto H. Leo. Diktat Persamaan Diferensial Parsial. Bandung: ITB
 Nagle, R.K., Saff, E.B., & Snider, A.D. (2012). Fundamental of Differential Equation and Boundary Value Problems. New York: Addison
 Hagni Wijayanti, dkk. (2011). Metode Runge-Kutta Dalam Penyelesaian Model Radang Akut. Bogor: UNPAK
Published
2022-04-15
How to Cite
ENKEKES, Yenci Brika; MARDIANTO, Lutfi. Metode Runge-Kutta Orde 4 Dalam Penyelesaian Persamaan Gelombang 1D Syarat Batas Dirichlet. Indonesian Journal of Applied Mathematics, [S.l.], v. 2, n. 1, p. 1-8, apr. 2022. ISSN 2774-2016. Available at: <https://journal.itera.ac.id/index.php/indojam/article/view/489>. Date accessed: 05 oct. 2022. doi: https://doi.org/10.35472/indojam.v2i1.489.
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