Algorithm 850: Real parabolic cylinder functions U(a,x), V(a,x)

Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions U(a, x), V (a, x) and their derivatives for real a and $x(xgeq 0)$. The code also computes scaled functions. The range of computation for scaled PCFs is practically unrestricted. The aimed relative accuracy for scaled functions is better than 5 10^{-14}. Exceptions to this accuracy are the evaluation of the functions near their zeros and the error caused by the evaluation of trigonometric functions of large arguments when |a| >> x. The routines always give values for which the Wronskian relation for scaled functions is verified with a relative accuracy better than $5 10^{?14}$. The accuracy of the unscaled functions is also better than $5 10 {?14}$ for moderate values of x and a (except close to the zeros), while for large x and a the error is dominated by exponential and trigonometric function evaluations. For IEEE standard double precision arithmetic, the accuracy is better than $5 10^{?13}$ in the computable range of unscaled PCFs (except close to the zeros).