PDP-10 Archive: decus/20-0026/qg4.doc from decus_20tap2

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SUBROUTINE QG4

PURPOSE
   TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU)

USAGE
   CALL QG4 (XL,XU,FCT,Y)
   PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT

DESCRIPTION OF PARAMETERS
   XL	  - THE LOWER BOUND OF THE INTERVAL.
   XU	  - THE UPPER BOUND OF THE INTERVAL.
   FCT	  - THE NAME OF AN EXTERNAL FUNCTION SUBPROGRAM USED.
   Y	  - THE RESULTING INTEGRAL VALUE.

REMARKS
   NONE

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED
   BY THE USER.

METHOD
   EVALUATION IS DONE BY MEANS OF 4-POINT GAUSS QUADRATURE
   FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 7
   EXACTLY.
   FOR REFERENCE, SEE
   V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS,
   MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-338.