Solution Of Three-Dimensional Helmholtz Equation By Using Triple Laplace Transform
DOI:
https://doi.org/10.63682/jns.v14i32S.7874Keywords:
Helmholtz equation, Triple Laplace Transform, Inverse Triple Laplace Transform, Partial differential equations.Abstract
The Helmholtz partial differential equation has various applications in the different fields such as electromagnetics, quantum mechanics, engineering, physics and its mathematical models power the technologies that are crucial in neonatal diagnostics, imaging, simulation, and intervention planning making it an essential tool in the computational background of advanced neonatal care. We present a novel approach to solving the Helmholtz equation using Triple Laplace Transform. An inversion of triple Laplace transforms has been achieved numerically by employing the Brancik technique. Numerical results are represented by graphically.
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A. Atangana, A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third-Order Differential Equation, Abstract and Applied Analysis (2013) 1-10.
T. Khan, K. Shah, A. Khan, R. Khan, Solution of fractional order heat equation via triple Laplace transform in 2 dimensions, Math Meth Appl Sci. (2017), 1–8.
D. A. Juraev, P. Agarwal, E. E. Elsayed, & N. Targyn, Helmholtz equations and their applications in solving physical problems, Advanced Engineering Science (2024) 54-64.
T. Alkhalifah, C. Song, U. Waheed, Q. Hao, Wavefield solutions from machine learned functions constrained by the Helmholtz equation, Artificial Intelligence in Geosciences (2021) 11-19.
H. Cheng and M. Peng, The Improved Element-Free Galerkin Method for 3D Helmholtz Equations, Mathematics (2022) 1-20.
Y. Chai, K. Huang, S. Wang, Z. Xiang and G. Zhang, The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation, Mathematics (2023) 1-25.
G. Bao, G.W. Wei and S. Zhao, Numerical solution of the Helmholtz equation with high wavenumbers, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2004) 389-408.
S. Gong, J. Martin, G. Ivan, L. David and A. Euan, Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation, Numerische Mathematik (2022) 259 - 306.
P. Roland and S. Olivier, The Helmholtz Equation with Uncertainties in the Wavenumber, Journal of Scientific Computing (2024) 1-24.
L. Brancik, Technique of 3D NILT based on complex Fourier series and quotient-difference algorithm, 17th IEEE International Conference on Electronics, Circuits and Systems (2010), 203 - 206.
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