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Explicit error bound for modified numerical iterated integration by means of Sinc methods
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.Comment: Keyword: Sinc quadrature, Sinc indefinite integration, repeated
integral, verified numerical integration, double-exponential transformatio