Relative Error Control in Bivariate Interpolatory Cubature

TL;DR

This paper presents an algorithm for controlling relative error in bivariate integral evaluation without prior magnitude knowledge, using positive-weight interpolatory quadrature, with numerical examples demonstrating its effectiveness.

Contribution

Introduces a novel algorithm for relative error control in bivariate interpolatory cubature that adapts to unknown integral magnitudes.

Findings

Algorithm effectively controls relative error without prior magnitude knowledge

Numerical examples demonstrate practical applicability

Suitable for integrals with unknown or small magnitudes

Abstract

We describe an algorithm for controlling the relative error in the numerical evaluation of a bivariate integral, without prior knowledge of the magnitude of the integral. In the event that the magnitude of the integral is less than unity, absolute error control is preferred. The underlying quadrature rule is positive-weight interpolatory and composite. Some numerical examples demonstrate the algorithm.