Optimization of quadrature formulas with derivatives

Аннотация

In this paper in the space ( ) 2 (0,1) m L the problem of construction of optimal quadrature formulas is considered. Here the quadrature sum consists on values of integrand at nodes and values of first, third, fifth and seventh derivatives of integrand at the end points of the integration interval. In the work the coefficients of the optimal quadrature formula are found and the norm of the error functional of the formula is calculated.