Gauss rules associated with nearly singular weights

Computation of Gauss-kronrod Quadrature Rules with Non-positive Weights

Recently Laurie presented a fast algorithm for the computation of (2n + 1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of Gauss-Kronrod quadrature rules with complex conjugate nodes and weights or with real nodes and positive and negative weights.

Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules

We show that the weights of extended Gauss-Legendre quadrature rules are all positive.

On Generalized Gaussian Quadrature Rules for Singular and Nearly Singular Integrals

We construct and analyze generalized Gaussian quadrature rules for integrands with endpoint singularities or near endpoint singularities. The rules have quadrature points inside the interval of integration and the weights are all strictly positive. Such rules date back to the study of Chebyshev sets, but their use in applications has only recently been appreciated. We provide error estimates an...

Gauss Integration Limits in Nearly Singular Integrals of BEM for Geometrically Linear Elements

The most suitable and widely used numerical integration method for boundary integrals in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing nearly singular integrals in the integral form of the Laplace equation. At the rst stage, a criterio...

Evaluating Singular and Nearly Singular Integrals Numerically