DOI: https://doi.org/10.36719/2663-4619/116/80-86
Naila Zakirli
Baku city, Khazar district, secondary school No. 156
https://orcid.org/0009-0009-1609-3284
naile.zakirli@gmail.com
Particular solutions of the Helmholtz equation and internal
boundary value problems
Abstract
This article examines the special solutions of the Helmholtz equation and the impact of internal boundary conditions (Neumann boundary conditions) on the behavior of the equation. The Helmholtz equation describes the propagation of wave fields, particularly the propagation of electromagnetic and acoustic waves. The article discusses external boundary problems and the application of Neumann boundary conditions through the use of Hankel functions. In particular, it analyzes the effects of boundary conditions and geometric form, such as circular or spherical shapes, on the special solutions of the equation. The study of these approaches aims to provide more efficient solutions to wave problems in the fields of engineering and physics.
Keywords: Helmholtz equation, Neumann boundary condition, Hankel functions, internal boundary, wave propagation, spherical coordinates, spectral analysis