Numerical solutions of generalized Abel integral and integro differential equations

Abstract

This paper introduced a numerical method for solving generalized Abel integral (GAI) equations and generalized Abel integro differential (GAID) equations. This method is based upon Touchard polynomials (TPs) approximation. The Touchard polynomials were first presented and the resulting Touchard matrices were utilized to transform the generalized Abel integral and integro differential equations into a system of linear algebraic equations. The results of the presented method were obtained through some examples of the first and second types of equations under study. All results for this method have been compared with those of the presented methods in the literature.

Subject Classification:

• 20C10
• 22E27

Keywords:

• Generalized Abel integral equation
• Generalized Abel integro differential equation
• Touchard polynomials
• Numerical solution
• Exact solution