## Algorithm 850

 swMATH ID: 4409 Software Authors: Gil, Amparo; Segura, Javier; Temme, Nico M. Description: 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 (x≥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). Homepage: http://dl.acm.org/citation.cfm?id=1132978 Related Software: BIZ; AIZ; Algorithm 914; DLMF; Algorithm 838; F1; FGH; Algorithm 858; NSWC; Algorithm 885; Algorithm 877; REMES2; Algorithm 822; Algorithm 861; Algorithm 644; Algorithm 855; Algorithm 804; NumSBT; Algorithm 682; Algorithm 814 Cited in: 5 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Algorithm 850: Real parabolic cylinder functions $$U(a, x)$$, $$V(a, x)$$. Zbl 1182.65039
Gil, Amparo; Segura, Javier; Temme, Nico M.
2006

### Cited by 4 Authors

 4 Gil, Amparo 4 Segura, Javier 4 Temme, Nico M. 1 Dunster, T. M.

### Cited in 3 Serials

 2 ACM Transactions on Mathematical Software 1 IMA Journal of Numerical Analysis 1 Journal of Classical Analysis

### Cited in 4 Fields

 4 Special functions (33-XX) 4 Numerical analysis (65-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX)