Hampiran Solusi Persamaan Gelombang Dua Dimensi Dengan Pendekatan Finite Difference

Mohamad Syafii, Muhammad Rafli Alghazali

Abstract


The finite difference method is widely used in determining the approximate solution of a time dependent partial differential equation. The purpose of this study is to calculate the numerical solution with a finite difference method to the two dimensional wave equation. The research method used is literature study. The solution of numerical problem using the finite difference method. Discretization the two-dimensional wave equation with a central difference approach. The second step, the discretization result is  simulated  by Matlab software. Based on the finite difference method result, the numerical solution approximates the analytical solution of the given two dimensional wave equation. The stability requirements of numerical solution using the finite difference method is the Von Nuemann stability.


Keywords


Error; Stability; Difference Method; Partial Differential Equation; Two Dimensional Wave Equation

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DOI: https://doi.org/10.15548/jostech.v2i1.3760
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References


K. Mahmoodi, H. Ghassemi, and A. Heydarian, “Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method,” Int. J. Partial Differ. Equations Appl., vol. 5, no. 1, pp. 19–25, 2017, doi: 10.12691/ijpdea-5-1-3.

A. Yasid and D. Handayani, “PENGARUH FREKUENSI GELOMBANG BUNYI TERHADAP PERILAKU LALAT RUMAH ( Musca domestica ),” J. Pembelajaran Fis., vol. 5, no. 2, pp. 190–196, 2011.

F. Mirzaee and S. Bimesl, “Results in Physics A new approach to numerical solution of second-order linear hyperbolic partial differential equations arising from physics and engineering n,” Results Phys., vol. 3, pp. 241–247, 2013, doi: 10.1016/j.rinp.2013.10.002.

S. Jung and S. Min, “Stability of the Wave Equation with a Source,” Hindawi J. Funct. Spaces, vol. 2018, no. 2, pp. 1–4, 2018, doi: https://doi.org/10.1155/2018/8274159.

W. A. Strauss, Partial Differential Equation (An Introduction). United States of America: John Wiley & Sons Inc, 2008.

R. Munir, Metode Numerik. Bandung: Informatika Bandung, 2008.

Hasan, T. Yulianto, R. Amalia, and Faisol, “Penerapan Metode Beda Hingga pada Model Matematika Aliran Banjir dari Persamaan Saint Venant,” Math J., vol. 2, no. 1, pp. 6–12, 2016.

B. S. Sasongko, Metode Numerik Dengan Scilab. Yogyakarta: CV. Andi Offset, 2010.

Y. A. Abdulkadir, “Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion,” J. Appl. Math. Phys., vol. 3, pp. 1544–1562, 2015, doi: http://dx.doi.org/10.4236/jamp.2015.311179.

A. J. M. Antunes, M. Sc, R. C. P. Leal-toledo, D. Sc, and O. Teixeira, “Finite Difference Method for Solving Acoustic Wave Equation Using Locally Adjustable Time-steps,” Procedia Comput. Sci., vol. 29, pp. 627–636, 2014, doi: 10.1016/j.procs.2014.05.056.

V. A. Riestiana, R. Setiyowati, and V. Y. Kurniawan, “Numerical solution of the one dimentional shallow water wave equations using finite difference method: Lax-Friedrichs scheme,” AIP Conf. Proc., vol. 2326, no. 02002, pp. 1–8, 2021, doi: 10.1063/5.0039545.

A. A. Noor, A. R. Putri, and M. Syafwan, “Solusi analitik dan numerik suatu persamaan gelombang satu dimensi,” J. Mat. UNAND, vol. VIII, no. 4, pp. 1–8, 2020.

M. Syafii, D. M. Putri, and A. Rahman, “Nullitas maksimum matriks hermitian digambarkan oleh graf g,” MAp (Mathematics Appl. J., vol. 3, no. I, pp. 53–61, 2021, doi: https://doi.org/10.15548/map.v3i1.2784.

W. Pandia and I. Sitepu, “Penentuan Galat Persamaan Diferensial Biasa Orde 1 dengan

Metode Numerik,” J. Mutiara Pendidik. Indones., vol. 6, no. 1, pp. 31–37, 2021, doi: https://doi.org/10.51544/mutiara%20pendidik.v6i1.1907.

A. Gopal, M. Mahdi, S. Jagdish, and C. Bansal, “On Stability Analysis of Particle Swarm Optimization Algorithm,” Arab. J. Sci. Eng., vol. 45, no. 4, pp. 2385–2394, 2020, doi: 10.1007/s13369-019-03991-8.


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