Title of article :
Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials
Author/Authors :
Talab Abdullah, Jalil College of Administration and Economics - Wasit University, Iraq , Sweedan Naseer, Bushra Institute of Medical Technology - Al-Mansour, Middle Technical University, Iraq , Taha Abdllrazak, Balasim College of Engineering - Al-Mustansiriya University, Iraq
Abstract :
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.
Keywords :
Abel integral equation , Numerical solution , singular Volterra , Touchard polynomials , Laguerre polynomials
Journal title :
International Journal of Nonlinear Analysis and Applications
