Amparo Gil
Abstract
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).
Supplemental Material
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Software for "Real parabolic cylinder functions U(a, x), V(a, x)"
- Gil, A., Segura, J., and Temme, N. M. 2004. Integral representations for computing real parabolic cylinder functions. Numer. Math. 98, 105--134. Google Scholar
- Gil, A. Segura, J., and Temme, N. M. Computing the Parabolic Cylinder Functions U(a, x), V(a, x). ACM Trans. Math. Soft., (in this issue). Google Scholar
- Segura, J. and Gil, A. 1998. Parabolic cylinder functions of integer and half-integer orders for non-negative arguments. Comput. Phys. Commun. 115, 69--86.Google Scholar
Index Terms
- Algorithm 850: Real parabolic cylinder functions U(a, x), V(a, x)
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