Lagrangian computational matrix approach to generalized abel's integral equation based on gauss-legendre roots

Abstract

In this work, our aim is to develop a numerical scheme for solving Generalized Abel's integral equation (GAIE). The proposed scheme is based upon Gauss Legendre roots as collocation node points over the Hilbert space defined on the domain [0,1]. To construct interpolating basis function (IBF), we used Lagrangian interpolating polynomial. Firstly, we introduced the function approximation by using generated IBF. The constructed approximation in pro-posed scheme is then converted the GAIE into the system of algebraic equation. The test functions clearly show the reliability and computational efficiency of the proposed method. © 2019, Institute of Advanced Scientific Research, Inc.. All rights reserved.