Algorithm 914: Parabolic Cylinder Function $W(a,x)$ and its Derivative

A Fortran 90 program for the computation of the real parabolic cylinder functions $W(a,\pm x),\,\,x\ge 0$ and their derivatives is presented. The code also computes scaled functions for $a>50$. The functions $W(a,\pm x)$ are a numerically satisfactory pair of solutions of the parabolic cylinder equation $y'' + \left(x^2/4 -a\right)y=0\,,\quad x\ge 0$. 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],[Gil et al. 2006b] completes the set of software for parabolic cylinder functions (PCFs) for real arguments.