Computation of Complex Airy Functions
Abstract
In this paper, we discuss an efficient way to evaluate scaled complex Airy functions by asymptotic series. By obtaining an a-priori estimate of the number of monotonically decreasing terms of the asymptotic series for exp (z1.5/1.5/)Ai(z) that can be summed without underflowing the unit round-off of the computer arithmetic, we avoid unnecessary computations during the summation. Using this method, we develop an efficient computational routine for obtaining numerically linearly independent Airy functions whose Wronskian is stable throughout the complex plane. The scaled complex Airy function of the second kind exp (-z1.5/1.5(Bi)(z) may be obtained with well-known connecting formulas from the numerically independent computations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 19, 1986
- Accession Number
- ADA630527
Entities
People
- Marvin J. Goldstein
Organizations
- Naval Underwater Systems Center