A new cubature formula with weight functions on the disc, with error estimates
For researchers in numerical integration, this provides a more accurate method for computing integrals over the disk with weight functions.
The paper introduces a new cubature formula for integrals over the disk with weight functions, achieving superior accuracy compared to standard methods, with error estimates supporting the performance.
We introduce a new type of cubature formula for the evaluation of an integral over the disk with respect to a weight function. The method is based on an analysis of the Fourier series of the weight function and a reduction of the bivariate integral into an infinite sum of univariate integrals. Several experimental results show that the accuracy of the method is superior to standard cubature formula on the disk. Error estimates provide the theoretical basis for the good performance of the new algorithm.