Explicit error bound for modified numerical iterated integration by means of Sinc methods

TL;DR

This paper improves a numerical iterated integration method by modifying its approximation formula for better convergence and providing explicit, computable error bounds, especially effective for product-type integrands.

Contribution

It introduces a modified approximation formula with enhanced convergence and derives explicit error bounds, advancing the numerical iterated integration technique.

Findings

Modified formula achieves better convergence rates.

Explicit error bounds are provided in a computable form.

Numerical examples confirm improved efficiency for product-type integrands.

Abstract

This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit error bound is given in a computable form for the modified formula. The formula works quite efficiently, especially if the integrand is of a product type. Numerical examples that confirm it are also presented.