**AUTHORS:**I. G. Burova, N. S. Domnin, A. E. Vezhlev, A. V. Lebedeva, A. N. Pakulina

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The present paper is devoted to the application of local polynomial integro-differential splines to the solution of integral equations, in particular, to the solution of the integral equations of Fredholm of the second kind. To solve the Fredholm equation of the second kind, we apply local polynomial integro-differential splines of the second and third order of approximation. To calculate the integral in the formulae of a piecewise quadratic integro-differential spline and piecewise linear integro-differential spline, we propose the corresponding quadrature formula. The results of the numerical experiments are given.

**KEYWORDS:**
polynomial splines, polynomial integro-differential splines, Fredholm equation

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