The use of Lavrentiev regularization method in Fredholm integral equations of the first kind. (English) Zbl 1469.45001

Altürk, Ahmet; Coşgun, Tahir

Int. J. Adv. Appl. Math. Mech. 7, No. 2, 70-79 (2019).

Summary: The Fredholm integral equations of the first kind are often considered as ill-posed problems. The conventional way of solving them is to first convert them into the Fredholm integral equations of the second kind by means of a regularization method. This is followed by applying some standard techniques that are available for solving Fredholm integral equations of the second kind. This combination of two methods usually has some significant drawbacks in the sense that it may not produce a solution or produces only one solution after tedious calculations. The aim of this study is to remove these impediments once and for all for separable kernels and provide a closed-form expression for obtaining one or infinitely many solutions using the Lavrentiev regularization method.

MSC:

45B05

Fredholm integral equations

Keywords:

regularization; Fredholm integral equation; ill-posed problems

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