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

作者：Gil Amparo^*; Segura Javier; Temme Nico M

来源：ACM Transactions on Mathematical Software, 2011, 38(1): 6.

DOI：10.1145/2049662.2049668

• Algorithms
• Parabolic cylinder functions
• ODE integration
• asymptotic expansions

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.

• 出版日期2011-11