Mathematical Modelling and Analysis (Mar 2023)
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.
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