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SUBROUTINE RKF65A (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKF6(5)A (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 fünfter und *
C siebenter Ordnung mit Schrittweiten-Kontrolle *
C page 93-106 *
C Computing 4 1969 *
C *
C*****************************************************************
C
C Declarations
C
DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
QG=5.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme)
C
COEFF(2,1)=1.0D0/6.0D0
COEFF(3,1)=4.0D0/15.0D0
COEFF(4,1)=2.0D0/3.0D0
COEFF(5,1)=4.0D0/5.0D0
COEFF(6,1)=1.0D0
COEFF(8,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/6.0D0
COEFF(3,2)=4.0D0/75.0D0
COEFF(4,2)=5.0D0/6.0D0
COEFF(5,2)=-8.0D0/5.0D0
COEFF(6,2)=361.0D0/320.0D0
COEFF(7,2)=-11.0D0/640.0D0
COEFF(8,2)=93.0D0/640.0D0
COEFF(3,3)=16.0D0/75.0D0
COEFF(4,3)=-8.0D0/3.0D0
COEFF(5,3)=144.0D0/25.0D0
COEFF(6,3)=-18.0D0/5.0D0
COEFF(8,3)=-18.0D0/5.0D0
COEFF(4,4)=5.0D0/2.0D0
COEFF(5,4)=-4.0D0
COEFF(6,4)=407.0D0/128.0D0
COEFF(7,4)=11.0D0/256.0D0
COEFF(8,4)=803.0D0/256.0D0
COEFF(5,5)=16.0D0/25.0D0
COEFF(6,5)=-11.0D0/80.0D0
COEFF(7,5)=-11.0D0/160.0D0
COEFF(8,5)=-11.0D0/160.0D0
COEFF(6,6)=55.0D0/128.0D0
COEFF(7,6)=11.0D0/256.0D0
COEFF(8,6)=99.0D0/256.0D0
COEFF(8,8)=1.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=7.0D0/1408.0D0
COEFF(2,5)=1125.0D0/2816.0D0
COEFF(2,6)=9.0D0/32.0D0
COEFF(2,7)=125.0D0/768.0D0
COEFF(3,4)=5.0D0/66.0D0
COEFF(3,5)=5.0D0/66.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=31.0D0/384.0D0
COEFF(1,3)=1125.0D0/2816.0D0
COEFF(1,4)=9.0D0/32.0D0
COEFF(1,5)=125.0D0/768.0D0
COEFF(1,6)=5.0D0/66.0D0
RETURN
END
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