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

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.

arXiv commentKeyword: Sinc quadrature, Sinc indefinite integration, repeated integral, verified numerical integration, double-exponential transformation