Geodesic
A method for solving the Fredholm integral equation of the first kind
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 113-125

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The paper considers a numerical method for solving the Fredholm integral equation of the first kind, the essence of which is to replace the original equation with the corresponding regularized equation of the second kind, which is then solved by the modified spline collocation method. The solution in this case is represented by a linear combination of minimal splines. The coefficients at the splines are computed using local approximation (in some cases, quasi-interpolation) methods. Results of numerical experiments are presented, which show that on model problems the proposed method results in sufficiently accurate approximations, and the use of minimal splines of a nonpolynomial form and related functionals can improve the approximation accuracy. 
@article{ZNSL_2022_514_a6,
     author = {E. K. Kulikov and A. A. Makarov},
     title = {A method for solving the {Fredholm} integral equation of the first kind},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--125},
     publisher = {mathdoc},
     volume = {514},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a6/}
}
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E. K. Kulikov; A. A. Makarov. A method for solving the Fredholm integral equation of the first kind. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 113-125. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a6/