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Manuscript Title: Two-dimensional adaptive quadrature over rectangular regions.
Authors: P.C. Lewellen
Program title: QADAPT
Catalogue identifier: AAZA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 27(1982)167
Programming language: Fortran.
Computer: SPERRY UNIVAC 1100/82.
Operating system: EXEC 8.
RAM: 33K words
Word size: 36
Keywords: General purpose, Quadrature, Adaptive, Multidimensional, Richardson extrapolation, Simplex.
Classification: 4.11.

Nature of problem:
Program QADAPT estimates the integral F of an arbitrary function f(x,y) over the unit square: F = integral 0-1 of integral 0-1 of f(x,y)dxdy. Any integral over a two-dimensional rectangular region may be written in this form. The value of F is computed to a specified relative accuracy and an error estimate is returned.

Solution method:
The program is an adaptation of the multidimensional algorithm developed by Kahaner and Wells. A more cautious extrapolation procedure and an error estimate suggested by Strom are used.

The extrapolation procedures used are strictly valid only for analytic integrands. Nevertheless, the program is generally reliable even if this requirement is violated at a finite number of points. Integration or rapidly varying or highly oscillatory functions may require more table space than specified in the test deck.

Unusual features:
The program provides adaptive subdivision of the region of integration and variable quadrature order. A global error reduction strategy guides the computation. Function values are stored using a double hashing technique for efficient reuse.

Running time:
Execution of two test cases which accompany this paper took approximately 0.7 CPU s.