Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
Optimal quadrature formulas with positive coefficients in L2(m)(0,1) space
Journal of Computational and Applied Mathematics
On an optimal quadrature formula in the sense of Sard
Numerical Algorithms
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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.