Interval enclosures for a certain class of multiple integrals

An interval algorithm for bounding multiple integrals of integrands f: R^n x R^m -> R^1 over compact rectangular regions in R^m is described. It is supposed that the limits of integration in R^m are constant, that x varies over a rectangular compact subset of R^n and that f(x, y) is continuously differentiable with respect to x and is either once, twice, or four times continuously differentiable with respect to y. A pseudocode Fortran 90 implementation of the algorithm is described and numerical results from Fortran 90 implementations of the algorithm are presented.