Double Integration Using One-Dimensional Adaptive Quadrature Routines: A Software Interface Problem

A software interface problem occurs when two or more items of software are used in conjunction with one another. If proper advantage of using good software is to be gained, the user has to connect them properly. In this paper the problem of double integration employing two similar one-dimensional adaptive quadrature routines is considered. If an absolute error no greater than epsilon/sub T/ in the final result is desired, it is necessary to determine what tolerance parameter epsilon/sub o/ to assign to the outer routine and what tolerance parameters epsilon/sub Ii/ to assign for calls to the inner routine. Since it is not known at the outset how many times the inner routine will be calledm there is required what is termed an accuracy-assignment strategy for determining epsilon/sub iI/. In this paper two simple accuracy assignment strategies are discussed in detail. It is shown that one of them can be unstable if the outer routine is constructed internally by one way (local error control), but that it is quite stable if it is constructed in another way (global error control). It is also found that one of the strategies is marginally more efficient for visually smooth integrands, while the othermore » is significantly more efficient for peaked integrands.« less