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SUBROUTINE RKF65B (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKF6(5)B (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 Some old and new Runge-Kutta formulas with *
C stepsize control and their error coefficients *
C page 265-270 *
C Computing 34 1985 *
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)=65.0D0/81.0D0
COEFF(6,1)=1.0D0
COEFF(7,1)=1.0D0/15.0D0
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)=-43745.0D0/26244.0D0
COEFF(6,2)=16539.0D0/13780.0D0
COEFF(7,2)=-409063.0D0/195000.0D0
COEFF(8,2)=231213.0D0/193180.0D0
COEFF(3,3)=16.0D0/75.0D0
COEFF(4,3)=-8.0D0/3.0D0
COEFF(5,3)=353860.0D0/59049.0D0
COEFF(6,3)=-204.0D0/53.0D0
COEFF(7,3)=124.0D0/75.0D0
COEFF(8,3)=-2820.0D0/743.0D0
COEFF(4,4)=5.0D0/2.0D0
COEFF(5,4)=-493675.0D0/118098.0D0
COEFF(6,4)=232595.0D0/69006.0D0
COEFF(7,4)=25357.0D0/8680.0D0
COEFF(8,4)=9512.525D3/2902.158D3
COEFF(5,5)=155155.0D0/236196.0D0
COEFF(6,5)=-91.0D0/636.0D0
COEFF(7,5)=-8928.0D0/1375.0D0
COEFF(8,5)=-5113.0D0/80244.0D0
COEFF(6,6)=314928.0D0/747565.0D0
COEFF(7,6)=79184.709D3/19394.375D3
COEFF(8,6)=584348.904D3/156152.2235D4
COEFF(8,8)=30800.0D0/2989.089D3
C
C A tilde values (see scheme)
C
COEFF(2,3)=167.0D0/2080.0D0
COEFF(2,5)=91375.0D0/229152.0D0
COEFF(2,6)=41.0D0/144.0D0
COEFF(2,7)=43046.721D3/269010.560D3
COEFF(3,4)=125.0D0/150192.0D0
COEFF(3,5)=743.0D0/9856.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=21.0D0/260.0D0
COEFF(1,3)=7625.0D0/19096.0D0
COEFF(1,4)=25.0D0/88.0D0
COEFF(1,5)=1594.323D3/9929.920D3
COEFF(1,6)=53.0D0/704.0D0
RETURN
END
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