1 2 SUBROUTINE DQK15(F,A,B,RESULT,ABSERR,RESABS,RESASC) 3C***BEGIN PROLOGUE DQK15 4C***DATE WRITTEN 800101 (YYMMDD) 5C***REVISION DATE 830518 (YYMMDD) 6C***CATEGORY NO. H2A1A2 7C***KEYWORDS 15-POINT GAUSS-KRONROD RULES 8C***AUTHOR PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. - 9C K. U. LEUVEN 10C DE DONCKER, ELISE, APPLIED MATH. AND PROGR. DIV. - 11C K. U. LEUVEN 12C***PURPOSE To compute I = Integral of F over (A,B), with error 13C estimate 14C J = integral of ABS(F) over (A,B) 15C***DESCRIPTION 16C 17C Integration rules 18C Standard fortran subroutine 19C Double precision version 20C 21C PARAMETERS 22C ON ENTRY 23C F - Double precision 24C Function subprogram defining the integrand 25C FUNCTION F(X). The actual name for F needs to be 26C Declared E X T E R N A L in the calling program. 27C 28C A - Double precision 29C Lower limit of integration 30C 31C B - Double precision 32C Upper limit of integration 33C 34C ON RETURN 35C RESULT - Double precision 36C Approximation to the integral I 37C Result is computed by applying the 15-POINT 38C KRONROD RULE (RESK) obtained by optimal addition 39C of abscissae to the7-POINT GAUSS RULE(RESG). 40C 41C ABSERR - Double precision 42C Estimate of the modulus of the absolute error, 43C which should not exceed ABS(I-RESULT) 44C 45C RESABS - Double precision 46C Approximation to the integral J 47C 48C RESASC - Double precision 49C Approximation to the integral of ABS(F-I/(B-A)) 50C over (A,B) 51C***REFERENCES (NONE) 52C***ROUTINES CALLED D1MACH 53C***END PROLOGUE DQK15 54 55 56