Article ID: MTJPAM-D-24-00207

Title: Classification and solution methods for Schlömilch-type integral equations

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00207; Volume 6 / Issue 3 / Year 2024, Pages 408-417

Document Type: Research Paper

Author(s): Ahmet Altürk ^a

^aDepartment of Mathematics, Amasya University, Amasya, Turkey

Received: 30 November 2024, Accepted: 22 January 2025, Published: 6 April 2025

Corresponding Author: Ahmet Altürk (Email address: ahmet.alturk@amasya.edu.tr)

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Abstract

Schlömilch’s integral equations are extensively used in the fields of terrestrial physics and ionospheric research. In recent years, numerous studies have focused on developing solution methods and exploring applications for these equations. In this work, we define, investigate, and propose a solution method for Schlömilch-type integral equations. We start by classifying Schlömilch-type integral equations and developing a simple yet effective method for solving each class. Additionally, we explore an application problem that leads to the Rayleigh equation and provide its solution. To demonstrate the efficiency and practicality of our findings, we include illustrative examples from the literature for each type of equation discussed.

Keywords: Integral equations, orthogonal polynomials, regularization

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