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DQG4.FOR
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1985-11-29
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49 lines
C
C ..................................................................
C
C SUBROUTINE DQG4
C
C PURPOSE
C TO COMPUTE INTEGRAL(FCT(X), SUMMED OVER X FROM XL TO XU)
C
C USAGE
C CALL DQG4 (XL,XU,FCT,Y)
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT
C
C DESCRIPTION OF PARAMETERS
C XL - DOUBLE PRECISION LOWER BOUND OF THE INTERVAL.
C XU - DOUBLE PRECISION UPPER BOUND OF THE INTERVAL.
C FCT - THE NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION
C SUBPROGRAM USED.
C Y - THE RESULTING DOUBLE PRECISION INTEGRAL VALUE.
C
C REMARKS
C NONE
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X)
C MUST BE FURNISHED BY THE USER.
C
C METHOD
C EVALUATION IS DONE BY MEANS OF 4-POINT GAUSS QUADRATURE
C FORMULA, WHICH INTEGRATES POLYNOMIALS UP TO DEGREE 7
C EXACTLY. FOR REFERENCE, SEE
C V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS,
C MACMILLAN, NEW YORK/LONDON, 1962, PP.100-111 AND 337-340.
C
C ..................................................................
C
SUBROUTINE DQG4(XL,XU,FCT,Y)
C
C
DOUBLE PRECISION XL,XU,Y,A,B,C,FCT
C
A=.5D0*(XU+XL)
B=XU-XL
C=.43056815579702629D0*B
Y=.17392742256872693D0*(FCT(A+C)+FCT(A-C))
C=.16999052179242813D0*B
Y=B*(Y+.32607257743127307D0*(FCT(A+C)+FCT(A-C)))
RETURN
END