Optimal Quadrature Formulas in the Sense of Sard in $W_2^{(m,m-1)}$ Space

TL;DR

This paper develops new optimal quadrature formulas in the Sobolev space $W_2^{(m,m-1)}$ using Sobolev's method, providing explicit coefficients and numerical validation of the theoretical results.

Contribution

It introduces a novel construction of optimal quadrature formulas in the specified Sobolev space with explicit coefficients derived via Sobolev's method.

Findings

Explicit formulas for optimal coefficients are obtained.

Numerical results confirm the theoretical optimality.

The method improves existing quadrature approaches in the space.

Abstract

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.