Interval Integration Revisited

Sérgio Galdino

Polytechnic School of Pernambuco University Rua Benfica, 455 - Madalena 50.750-470 - Recife - PE - Brazil.

DOI: 10.4236/ojapps.2012.24B026                

Abstract

We present an overview of approaches to selfvalidating one-dimensional integration quadrature formulas and a verified numerical integration algorithm with an adaptive strategy. The new interval integration adaptive algorithm delivers a desired integral enclosure with an error bounded by a specified error bound. The adaptive technique is usually much more efficient than Simpson’s rule and narrow interval results can be reached.

Keywords

Interval computing, self-validating methods, numerical integration & interval arithmetic

Conflicts of Interest

The authors declare no conflicts of interest.

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