Optimal quadrature formulas with the trigonometric weight in the Sobolev space
A.R. Hayotov, Bakhromjon Bozarov
Abstract
In this paper there is considered the problem of construction of a new optimal quadrature formula in the sense of Sard in L2(m) 0,1] Hilbert space, using S.L. Sobolev’s method. There are given explicit formulas for coefficients of the optimal quadrature formula. Furthermore, some numerical results are presented.
Topics & Concepts
Sobolev spaceQuadrature (astronomy)MathematicsTrigonometryGauss–Kronrod quadrature formulaGauss–Jacobi quadratureClenshaw–Curtis quadratureMathematical analysisTanh-sinh quadratureHilbert spaceGauss–Laguerre quadratureNumerical integrationGaussian quadratureApplied mathematicsNyström methodIntegral equationPhysicsOpticsMathematical functions and polynomialsDifferential Equations and Boundary ProblemsIterative Methods for Nonlinear Equations