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Explicit Error Bound for Modified Numerical Iterated Integration by Means of Sinc Methods

  • Tomoaki OkayamaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

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) an 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.

Keywords

Sinc quadrature Sinc indefinite integration Repeated integral Verified numerical integration Double-exponential transformation 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Hiroshima City UniversityAsaminami-kuJapan

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