TITLE:
Spectral Analysis of the Derivation of Green’s Function of Helmholtz Integral Equation via Dirac-Delta Function and Cauchy Residual Approach
AUTHORS:
Md. Shuzon Ali, Sherajum Monira Bristy, Md. Abdullah Al Asad, Nur Hasan Mahmud Shahen
KEYWORDS:
Helmholtz Integral Equation, Summerfield Radiation Condition, Cauchy Residual Approach, Classical Schrödinger Wave Equation, Green’s Function
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.6,
June
14,
2023
ABSTRACT: In this study, we have determined Green’s functions for Helmholtz integral equations in a spherical polar coordinate system in the whole plane domain with the aid of spectral Fourier transform technique. Our intended Green’s function solution has a dominant role to represent wave propagation with a high quantum wave number. The Diracdelta function also plays an important role here to represent the scattering region for wave propagation. The evaluation of the improper double integrals in the complex plane furnishes our desired Green’s functions. The applied technique allows us to obtain all of the possible Green’s functions by using Somerfield radiation condition. With the help of computational software package MATLAB, we have drawn the solution plot that can express the analogue of wave propagation features. By using the MATLAB software package, we have drawn the solution plot that can express the analogue of wave propagation features.