Automatic Quadrature with Conditionally Activated Extended Clenshaw-Curtis Rules.

摘要

Quadrature rules of the extended Clenshaw-Curtis (ECC) type are derived for integrands with trigonometric or hyperbolic weight functions. The study puts into evidence the existence of a fully analytic solution, in terms of hypergeometric functions /sub 0/F/sub 1/. An important implementation problem, namely the possibility of conditional activation of the ECC, is evidenced and solved. As compared with the best available similar code (QUADPACK, by Piessens et al.), our resulting code is sensibly faster, requires a significantly smaller overhead, while yielding a fully reliable output. (author). 13 refs, 6 tabs. (Atomindex citation 19:059912)