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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.

Restrictions:
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.