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