A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme

Abstract

To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.

Keywords

• ill-posed problems
• iterative regularization scheme
• Legendre collocation method
• integral equations of the first kind