Metode Backward Time Central Space dalam Penyelesaian Model Matematika Vibrasi Dawai pada Alat Musik Petik

Atik Damayanti, Ari Kusumastuti, Nurul A. Hidayati

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).

Keywords

String Vibration stringed instrument; Numerical Simulate; String Deviation; Implicit Method; Backward Time Central Space; u(x;t) Solution

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References

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DOI: https://doi.org/10.18860/jrmm.v1i4.14454

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