Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials

Document Type : Research Paper


1 College of Administration and Economics, Wasit University, Iraq

2 Institute of Medical Technology, Al-Mansour, Middle Technical University, Iraq

3 College of Engineering, Al-Mustansiriya University, Iraq


In this article, two numerical methods based on Touchard and Laguerre polynomials were presented to solve Abel integral (AI) equations. Touchard and Laguerre matrices were utilized to transform Abel integral equations into an algebraic system of linear equations. Solve this system of these equations to obtain Touchard and Laguerre parameters. Four examples are given to demonstrate the presented methods. The solutions were compared with the solutions in the literature.