Author(s):
1. Prashant Kadam:
Department of Engineering Science, Bharati Vidyapeeth's College of Engineering Lavale,Pune,India
2. Atish Mane:
Department of Mechanical Engineering, Bharati Vidyapeeth's College of Engineering Lavale,Pune,India
3. Rakeyshh Byakuday:
Science and Humanity Department, DKTE'S Yashwantrao Chavan Polytechnic,Ichalkaranji,India
4. Neeraj Gangurde:
Department of Civil Engineering, Bharati Vidyapeeth's College of Engineering Lavale,Pune,India
5. Shrikant Nangare:
Department of General Science, D.Y. Patil Technical Campus Faculty of Engineering & Faculty of Management,Talsande,India
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.
Page(s):
701-706
DOI:
DOI not available
Published:
Journal: ARPN Journal of Engineering and Applied Sciences, Volume: 19, Issue: 11, Year: 2024
Keywords:
Accuracy
,
stability
,
Numerical analysis
,
finite element method
,
mathematical modeling
,
efficiency
,
partial differential equation
,
Finite difference method
,
one and twodimensional waves
,
wave equations
,
spectral method
References:
[1] Time-Dependent Problems by Randall J. LeVeque ,Society . .Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and. , 43 : .
Citations
Citations are not available for this document.