OPTIMAL QUADRATURE FORMULAS FOR FOURIER COEFFICIENTS IN W2(m,m-1) 2 SPACE
| Autor: | Gradimir V. Milovanović, Kholmat M. Shadimetov, Nurali D. Boltaev, Abdullo R. Hayotov |
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| Rok vydání: | 2017 |
| Předmět: |
Quadrature domains
General Mathematics Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Gauss–Kronrod quadrature formula Tanh-sinh quadrature Quadrature (mathematics) 010101 applied mathematics Sobolev space Gauss–Jacobi quadrature 0101 mathematics Fourier series Mathematics Clenshaw–Curtis quadrature |
| Zdroj: | Journal of Applied Analysis & Computation. 7:1233-1266 |
| ISSN: | 2156-907X |
| DOI: | 10.11948/2017076 |
| Popis: | This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the W2(m,m-1)[0,1] space for calculating Fourier coefficients. Using S. L. Sobolev's method we obtain new optimal quadrature formulas of such type for N + 1 ≥ m, where N + 1 is the number of the nodes. Moreover, explicit formulas for the optimal coefficients are obtained. We investigate the order of convergence of the optimal formula for m=1. The obtained optimal quadrature formula in the W2(m,m-1)[0,1] space is exact for exp(-x) and Pm-2(x), where Pm-2(x) is a polynomial of degree m -2. Furthermore, we present some numerical results, which confirm the obtained theoretical results |
| Databáze: | OpenAIRE |
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