THE EXISTENCE OF A FINITE-DIMENSIONAL SOLUTION NONLINEAR INTEGRAL FREDHOLM EQUATION OF THE FIRST KIND

а. СААДАБАЕВ, A.R. Abdyldaeva

2020

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DOI 10.35803/1694-5298.2020.3.459-466
Data confidence 70 medium
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Abstract

In this paper, the existence of a finite-dimensional solution of a nonlinear integral equation is proved when the right-hand side and the kernel are given approximately. A finite-dimensional regularizing operator is constructed, and it is proved that for n → ∞ and for a special choice of the parameter n from δ, the solution of the finite-dimensional problem converges to the exact solution of the original equation. It is shown by an example that using the Green's function it is possible to approximate a differential operator by an integral operator.