Chebyshev-Type Quadrature Formulas for New Weight Classes

TL;DR

This paper develops Chebyshev-type quadrature formulas for new weight classes, achieving optimal degree with a constructive node description, motivated by applications like the Faraday cage phenomenon.

Contribution

Introduces Chebyshev-type quadrature formulas for novel weight classes with maximal degree for node counts as powers of two, including a constructive method for node determination.

Findings

Formulas achieve highest possible degree for given nodes.

Nodes are described constructively for practical application.

Applications include modeling the Faraday cage phenomenon.

Abstract

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.