Algorithm 914

Abstract

A Fortran 90 program for the computation of the real parabolic cylinder functions W ( a , ± x ), x ≥ 0 and their derivatives is presented. The code also computes scaled functions for a > 50. The functions W ( a , ± x ) are a numerically satisfactory pair of solutions of the parabolic cylinder equation y ′ + ( x 2 /4 − a ) y = 0, x ≥ 0. Using Wronskian tests, we claim a relative accuracy better than 5 10 −13 in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than 5 10 −14 . This code, together with the algorithm and related software described in Gil et al. [2006a, 2006b], completes the set of software for Parabolic Cylinder Functions (PCFs) for real arguments.