Cubature Formulae Using Interlineation of Functions

Ivan V. Sergienko (), Valeriy K. Zadiraka () and Oleg M. Lytvyn ()
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Ivan V. Sergienko: National Academy of Sciences of Ukraine
Valeriy K. Zadiraka: National Academy of Sciences
Oleg M. Lytvyn: Ukrainian Engineering Pedagogics Academy

Chapter Chapter 5 in Elements of the General Theory of Optimal Algorithms, 2021, pp 253-280 from Springer

Abstract: Abstract This chapter presents the cubature formulas for calculating the integrals of the functions of two variables, which are obtained by replacing the subintegral function by spline interlineation operators. The cubature formulas for calculating the integrals of fast-oscillating functions are also given, in which the non-oscillating factor is replaced by the corresponding spline interlineation formula. Here using integral representations of the residual terms of the approximation of differentiation functions of two and three variables with and without preservation of the class of differentiation. Creating application software sometimes costs more than the cost of the computer itself. Therefore, testing the quality of software is a very important task.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-90908-6_5

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DOI: 10.1007/978-3-030-90908-6_5

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