Abstract
This paper discusses the construction of polynomialand non-polynomial splines of the fourth order of approximation.The behavior of the Lebesgue constants for the left, the right, andthe middle continuous cubic polynomial splines are considered.The non-polynomial splines are used for the construction of thespecial central difference approximation. The approximation offunctions, and the solving of the boundary problem with thepolynomial and non-polynomial splines are discussed. Numericalexamples are done.
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