Solution Of Three-Dimensional Helmholtz Equation By Using Triple Laplace Transform - Gothankar, Ranjana; Agrawal, Bhawna; Sankeshwari, Sagar (Journal of Neonatal Surgery, 2025)
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.