Optimal quadrature formulas for computing of Fourier integrals in W2(m,m−1) space
Abdullo Hayotov, Samandar Babaev
Abstract
In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_a^b e^{2\pi i\omega x}\varphi(x)d x$ with $\omega\in \mathbb{R}$ in the Hilbert space $W_2^{(2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.
Topics & Concepts
MathematicsQuadrature (astronomy)Gauss–Kronrod quadrature formulaNumerical integrationClenshaw–Curtis quadratureTanh-sinh quadratureGauss–Hermite quadratureGauss–Laguerre quadratureGauss–Jacobi quadratureHilbert spaceMathematical analysisApplied mathematicsFourier seriesFourier transformSpace (punctuation)Gaussian quadratureFourier analysisNumerical analysisCalculus (dental)Adaptive quadratureTrigonometric integralMathematical functions and polynomialsMathematical Inequalities and ApplicationsNumerical methods in engineering