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SUBROUTINE RKF54 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKF5(4) (method of Fehlberg). *
C *
C *
C INPUT PARAMETERS: *
C ================= *
C M : Dimension of the matrix COEFF depending on the chosen*
C embedding formula *
C *
C *
C OUTPUT PARAMETERS: *
C ================== *
C COEFF : 2-dimensional DOUBLE PRECISION array COEFF(1:16,1:M) *
C with the coefficients for the embedding formula *
C QG : DOUBLE PRECISION value for the global error order *
C *
C *
C----------------------------------------------------------------*
C *
C required subroutines: none *
C *
C*****************************************************************
C *
C Author : Volker Krüger *
C Date : 26.04.1993 *
C Source : FORTRAN 77 *
C Sources : E. Fehlberg : *
C Klassische Runge-Kutta-Formeln vierter und *
C niedrigerer Ordnung mit Schrittweiten-Kontrolle *
C und ihrer Anwendung auf Wärmeleitungsprobleme *
C page 61-71 *
C Computing 6 1970 *
C *
C*****************************************************************
C
C Declarations
C
DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
QG=4.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme)
C
COEFF(2,1)=1.0D0/4.0D0
COEFF(3,1)=3.0D0/8.0D0
COEFF(4,1)=12.0D0/13.0D0
COEFF(5,1)=1.0D0
COEFF(6,1)=1.0D0/2.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/4.0D0
COEFF(3,2)=3.0D0/32.0D0
COEFF(4,2)=1932.0D0/2197.0D0
COEFF(5,2)=439.0D0/216.0D0
COEFF(6,2)=-8.0D0/27.0D0
COEFF(3,3)=9.0D0/32.0D0
COEFF(4,3)=-7200.0D0/2197.0D0
COEFF(5,3)=-8.0D0
COEFF(6,3)=2.0D0
COEFF(4,4)=7296.0D0/2197.0D0
COEFF(5,4)=3680.0D0/513.0D0
COEFF(6,4)=-3544.0D0/2565.0D0
COEFF(5,5)=-845.0D0/4104.0D0
COEFF(6,5)=1859.0D0/4104.0D0
COEFF(6,6)=-11.0D0/40.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=16.0D0/135.0D0
COEFF(2,5)=6656.0D0/12825.0D0
COEFF(2,6)=28561.0D0/56430.0D0
COEFF(3,4)=-9.0D0/50.0D0
COEFF(3,5)=2.0D0/55.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=25.0D0/216.0D0
COEFF(1,3)=1408.0D0/2565.0D0
COEFF(1,4)=2197.0D0/4104.0D0
COEFF(1,5)=-1.0D0/5.0D0
RETURN
END
Begin of file
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