Optimal Quadrature Formulas in the Sense of Sard in $W_2^{(m,m-1)}$ Space
arXiv:1010.517249 citationsh-index: 20
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This is an incremental theoretical contribution to numerical integration for a specific function space.
The paper constructs a new optimal quadrature formula in the sense of Sard for the $W_2^{(m,m-1)}(0,1)$ space using Sobolev's method, providing explicit formulas for the optimal coefficients and numerical validation.
In this paper in $W_2^{(m,m-1)}(0,1)$ space the problem of construction of optimal quadrature formula in the sense of Sard is considered and using S.L. Sobolev's method it is obtained new optimal quadrature formula of such type. For the optimal coefficients explicit formulas are obtained. Furthermore, the numerical results which confirm the theoretical results of this work is given.