Approximation theory

Daghestan Electronic Mathematical Reports: Issue 17 (2022)

On the approximate solution of the Fredholm's integral equations by the method of collocation rational spline functions

UDK: 519.64+519.65

Pages: 20 - 31

For arbitrary grids of nodes, an approximate solution of the integral equation Fredholm of the second kind in the form of a collocation rational spline function is obtained. Estimates of the rate of uniform convergence of approximate solutions to the exact solution from the smoothness class $C^r$ for $r=0,1,2$ are presented.

Keywords: rational spline-function, interpolating spline functions, Fredholm integral equations, approximate solution of integral equations.

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