Interpolant Method in Analyzing the Laser-Induced Plasma Spectroscopy

Abstract

A numerical algorithm that effectively solves the Abel integral equation in laser-induced plasma spectroscopy is introduced. The proposed algorithm utilizes a barycentric interpolation and a collocation method with second-kind Chebyshev nodes. This approach reduces the Abel integral equation to a linear system of equations, resulting in efficient approximate solutions. Analytical studies provide an error estimation for the proposed method, which further validates its effectiveness. Through numerical experiments, we demonstrate the ease of implementation and showcase the efficiency of the proposed method. Our results indicate that the proposed algorithm can provide valuable insight for researchers in the field of laser-induced plasma spectroscopy and beyond.