A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme. (English) Zbl 07706391
Summary: 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.
MSC:
| 47A52 | Linear operators and ill-posed problems, regularization |
| 65R30 | Numerical methods for ill-posed problems for integral equations |
Keywords:
ill-posed problems; iterative regularization scheme; Legendre collocation method; integral equations of the first kindReferences:
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