An error estimate for the Gauss-Jacobi-Lobatto quadrature rule

TL;DR

This paper derives an error estimate for the Gauss-Lobatto quadrature rule when integrating functions with Jacobi weights over [-1, 1], applicable to certain Sobolev-type function spaces.

Contribution

It provides a new error estimate for the Gauss-Lobatto quadrature with Jacobi weights, extending understanding of its accuracy for Sobolev-type functions.

Findings

Error estimate established for Gauss-Lobatto quadrature with Jacobi weights.

Applicable to functions in specific Sobolev-type subspaces.

Enhances understanding of quadrature accuracy for weighted Sobolev spaces.

Abstract

An error estimate for the Gauss-Lobatto quadrature formula for integration over the interval $[-1, 1]$, relative to the Jacobi weight function $w^{\alpha,\beta}(t)=(1-t)^\alpha(1+t)^\beta$, $\alpha,\beta>-1$, is obtained. This estimate holds true for functions belonging to some Sobolev-type subspaces of the weighted space $L_{w^{\alpha,\beta}}^1([-1,1])$.