Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials

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.

کلیدواژه ها:

Abel integral equation ، Numerical Solution ، singular Volterra ، Touchard polynomials ، Laguerre polynomials