A numerical study of the wave equation and mathematical modeling of the wave equation using numerical analysis
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Full Text |
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Author |
Prashant Kadam, Atish Mane, Rakeyshh Byakuday, Neeraj Gangurde and Shrikant Nangare
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e-ISSN |
1819-6608 |
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On Pages
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701-706
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Volume No. |
19
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Issue No. |
11
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Issue Date |
August 15, 2024
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DOI |
https://doi.org/10.59018/062492
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Keywords |
finite difference method, wave equations, partial differential equation, one and two-dimensional waves, mathematical modeling, numerical analysis, finite element method, spectral method, accuracy, stability, efficiency.
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Abstract
The wave equation, a partial differential equation that defines how waves propagate in a variety of physical systems, including fluid dynamics, acoustics, and electromagnetic, is the subject of our study and investigation in this research work. In this paper, we investigate the wave equation using mathematical models and numerical analysis. We first review the mathematical theory behind the wave equation, including its derivation and solution. Next, to resolve the equation for waves numerically, we provide finite difference and finite element approaches. We also prefer the numerical outcomes with the analytical solutions to verify the accuracy of the numerical methods. We present a mathematical model of the wave equation using numerical analysis. The operation of waves in many physical systems is described by the wave equation, which is a partial differential equation. We first introduce the wave equation and its physical meaning. We then go over and use the finite difference approach to solve the wave equation and other partial differential equations. After that, we go over the numerical method's stability and convergence and show numerical findings to support our theory. Our findings demonstrate the efficacy of the numerical approach in resolving the wave equation.
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