OPTIMAL QUADRATURE FORMULA WITH DERIVATIVE FOR APPROXIMATING INTEGRALS AND SOLVING INTEGRAL EQUATIONS IN SOBOLEV SPACE
DOI:
https://doi.org/10.55640/Keywords:
Sobolev space, quadrature formulas, extremal function, norm of the error functional, optimal coefficients.Abstract
As a result of extensive scientific research conducted on a global scale, the numerical solution of exact integrals in the problems of solar physics, modeling of synthesized holograms, mechanics of liquids and gases with high accuracy leads to the construction of optimal quadrature formulas. Usually, the use of simple interpolation quadrature formulas in solving such problems requires a large amount of computational work. The effectiveness of quadrature formulas is characterized by their degree of accracy and order of accuracy. In this work, the derivative optimal quadrature formula is constructed using the first and second order derivatives of the function at the nodes in the real-valued Sobolev space of the differentiable functions.
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