An Adaptive Numerical Integration Algorithm with Automatic Result Verification for Definite Integrals

Abstract

We present a verified numerical integration algorithm with an adaptive strategy for smooth integrands. Verified representations of the remainder term are derived and a new adaptive strategy is given which delivers a desired integral enclosure with an error usually bounded by a specified error bound. Here, we discuss the distribution of the specified error bound onto the subintervals used in the algorithm more closely and present numerical results depending on the distribution of the error.