Discrete Hybrid Polyharmonic Cubature Formulas with weight on the disc. with error bounds

TL;DR

This paper advances discrete polyharmonic cubature formulas on the disc by optimizing precision and efficiency, providing a more effective numerical integration method with established error bounds.

Contribution

It introduces a refined cubature formula with improved accuracy and efficiency, completing the authors' previous work on discrete polyharmonic cubature on the disc.

Findings

Enhanced cubature formulas with better precision

Reduced number of evaluation points needed

Established error bounds for the formulas

Abstract

This paper is a second part of our study of the Discrete Polyharmonic Cubature Formulas on the disc. It completes our study and provides a satisfactory cubature formula in terms of precision and number of evaluation points (coefficient of efficiency of the formula).