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

Abstract
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 mo...

Title of program: cuspint
Catalogue Id: ADMP_v1_0

Nature of problem
The theoretical treatment of short wavelength scattering phenomena often involves the uniform asymptotic evaluation of oscillating integrals with several coalescing saddle points. An important practical problem then is the numerical evaluation of the cuspoid canonical integrals and their first order partial derivatives.

Versions of this program held in the CPC repository in Mendeley Data
ADMP_v1_0; cuspint; 10.1016/S0010-4655(00)00126-0

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
我们提出了一段用于计算振荡尖点正则积分（oscillatory cuspoid canonical integrals）及其一阶偏导数（first order partial derivatives）的代码。本算法基于Connor与Curtis提出的方法[J. Phys. A 15 (1982) 1179–1190]，该方法将实轴上的积分路径替换为复平面中更便于计算的围道，使得振荡被积函数更适合数值求积运算。本代码是该方法的现代化实现，以模块化形式呈现为Fortran 90语言的……

程序名称：cuspint
目录编号：ADMP_v1_0

问题本质
短波长散射现象的理论处理通常涉及对带有多个汇聚鞍点的振荡积分进行一致渐近求值，而其中一项重要的实际问题便是对尖点正则积分及其一阶偏导数进行数值求值。

存放在Mendeley数据的CPC程序库中的该程序版本
ADMP_v1_0; cuspint; 10.1016/S0010-4655(00)00126-0

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）