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Atik Damayanti
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Mathematics

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Metode Backward Time Central Space dalam Penyelesaian Model Matematika Vibrasi Dawai pada Alat Musik Petik Atik Damayanti; Ari Kusumastuti; Nurul A. Hidayati
Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (442.168 KB) | DOI: 10.18860/jrmm.v1i4.14454

Abstract

This research was conducted to obtain a numerical solution of the mathematical model of string vibration on stringed instruments. This mathematical model is a representation of the phenomenon of string vibration on a stringed instrument subject to deviation. The model was constructed by Kusumastuti, et al (2017) and is in the form of a second-order partial differential equation. The method used in completing this research is the BTCS (Backward Time Central Space) method. The numerical solution is obtained by the following steps, 1). Discretize mathematical models, as well as discretize initial conditions and boundary conditions. 2). Performing stability analysis of numerical solutions to determine the terms of solution stability and conducting consistency analysis as a condition of the convergence of the obtained numerical solutions. 3). Simulate numerical solutions and perform graph interpretations. The results show that the numerical solution of the mathematical model of string vibration on stringed instruments is unconditionally stable and has an error order (〖∆x〗^2,〖∆t〗^3).
Co-Authors Ari Kusumastuti Nurul A. Hidayati