An efficient method for solving Schlömilch-type integral equations

Abstract

Schlömilch integral equations have many applications in terrestrial physics and serve as useful tools for various ionospheric problems. Recently, researchers have investigated Schlömilch-type integral equations. Unlike Schlömilch integral equations, there are only a few works in the literature that discuss the classification and solution methods for Schlömilch -type equations. In this study, we mainly focus on introducing an efficient method based on a modified homotopy approach for solving certain Schlömilch-type equations. To demonstrate the efficiency and simplicity of the proposed algorithm, we also present some extensions that enable the solution of important application-related problems.

Keywords

• Fredholm integral equations
• homotopy
• perturbation theory
• Rayleigh equation

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