Name
Abstract | ||
|---|---|---|
This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L"2^(^m^)(0,1). In this paper the quadrature sum consists of values of the integrand at nodes and values of the first derivative of the integrand at the end points of the integration interval. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number N and for any m=2 using the S.L. Sobolev method which is based on a discrete analog of the differential operator d^2^m/dx^2^m. In particular, for m=2,3 optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from m=4 new optimal quadrature formulas are obtained. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.cam.2012.11.010 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
sobolev method,classical euler-maclaurin quadrature formula,quadrature sum,optimal quadrature formula,optimal error,arbitrary natural number,paper study,differential operator,sobolev space l2,discrete analog,new optimal quadrature formula,sobolev space,numerical analysis | Gauss–Kronrod quadrature formula,Mathematical optimization,Mathematical analysis,Numerical integration,Tanh-sinh quadrature,Clenshaw–Curtis quadrature,Gauss–Hermite quadrature,Quadrature domains,Gauss–Jacobi quadrature,Mathematics,Gauss–Laguerre quadrature | Journal |
Volume | ISSN | Citations |
243, | 0377-0427 | 1 |
PageRank | References | Authors |
0.40 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kh. M. Shadimetov | 1 | 5 | 1.70 |
| Abdullo Rakhmonovich Hayotov | 2 | 9 | 4.58 |
| F. A. Nuraliev | 3 | 1 | 0.73 |