An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives

• Published in: Computer physics communications 2000-10, Vol.132 (1), p.142-165
• Main Authors: Kirk, N.P., Connor, J.N.L., Hobbs, C.A.
• Format: Article
• Language: English
• Subjects: Atomic and molecular collision processes and interactions; Atomic and molecular physics; Computational techniques; Exact sciences and technology; Function theory, analysis; Functions of a complex variable; General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.); Mathematical methods in physics; Physics; Several complex variables and analytic spaces; Special functions
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(00)00126-0

We present a code to compute the oscillatory cuspoid canonical integrals and their first order partial derivatives. The algorithm is based on the method of Connor and Curtis [J. Phys. A 15 (1982) 1179–1190], in which the integration path along the real axis is replaced by a more convenient contour in the complex plane, rendering the oscillatory integrand more amenable to numerical quadrature. Our code is a modern implementation of this method, presented in a modular fashion as a Fortran 90 module containing the relevant subroutines. The code is robust, with the novel feature that the algorithm implements an adaptive contour procedure, choosing contours that avoid the violent oscillatory and exponential natures of the integrand and modifying its choice as necessary. In many cases, the subroutines are efficient and provide results of high accuracy. Plots and results for the Pearcey and swallowtail cuspoid integrals given in previous articles are reproduced and verified. Our subroutines significantly extend the range of application of this earlier work.