Advanced Mathematical Models & Applications

In this paper, to solve the ill-posed integral equations, we employ the regularized Legendre-collocation method. A new numerical method is proposed that is a combination of the Legendre-Collocation method i.e., a numerical method based on the collocation projection method, where the solution is projected onto a subspace generated by Legendre orthogonal polynomials and the Tikhonov regularization procedure. The mail feature of the proposed approach is that here orthogonal Legendre polynomials are employed to approximate a solution for an unknown function in the Fredholm integral equation and convert the equation to a system of linear algebraic equations. The accuracy and efficiency of this method are illustrated through numerical examples.