15. Numerical Integration

This chapter describes routines for performing numerical integration (quadrature) of a function in one dimension. There are routines for adaptive and non-adaptive integration of general functions, with specialised routines for specific cases. These include integration over infinite and semi-infinite ranges, singular integrals, including logarithmic singularities, computation of Cauchy principal values and oscillatory integrals. The library reimplements the algorithms used in QUADPACK, a numerical integration package written by Piessens, Doncker-Kapenga, Uberhuber and Kahaner. Fortran code for QUADPACK is available on Netlib.

The functions described in this chapter are declared in the header file `gsl_integration.h'.

15.1 Introduction
15.2 QNG non-adaptive Gauss-Kronrod integration
15.3 QAG adaptive integration
15.4 QAGS adaptive integration with singularities
15.5 QAGP adaptive integration with known singular points
15.6 QAGI adaptive integration on infinite intervals
15.7 QAWC adaptive integration for Cauchy principal values
15.8 QAWS adaptive integration for singular functions
15.9 QAWO adaptive integration for oscillatory functions
15.10 QAWF adaptive integration for Fourier integrals
15.11 Error codes
15.12 Examples
15.13 References and Further Reading