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SUBROUTINE RKF43 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKF4(3) (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=3.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (refer to the coefficient schemes in chapter 17.3.4.4)
C ( similarly below )
C
COEFF(2,1)=2.0D0/7.0D0
COEFF(3,1)=7.0D0/15.0D0
COEFF(4,1)=35.0D0/38.0D0
COEFF(5,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=2.0D0/7.0D0
COEFF(3,2)=77.0D0/900.0D0
COEFF(4,2)=805.0D0/1444.0D0
COEFF(5,2)=79.0D0/490.0D0
COEFF(3,3)=343.0D0/900.0D0
COEFF(4,3)=-77175.0D0/54872.0D0
COEFF(4,4)=97125.0D0/54872.0D0
COEFF(5,4)=2175.0D0/3626.0D0
COEFF(5,5)=2166.0D0/9065.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=79.0D0/490.0D0
COEFF(2,5)=2175.0D0/3626.0D0
COEFF(3,4)=2166.0D0/9065.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=229.0D0/1470.0D0
COEFF(1,3)=1125.0D0/1813.0D0
COEFF(1,4)=13718.0D0/81585.0D0
COEFF(1,5)=1.0D0/18.0D0
RETURN
END
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