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SUBROUTINE RK658M (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RK6(5)8M (method of Dormand und Prince). *
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 : J. R. Dormand P. J. Prince : *
C High order embedded Runge-Kutta formulae *
C page 67-75 *
C Journal of Computational and Applied Mathematics, *
C volume 7, no 1, 1981 *
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)=1.0D0/10.0D0
COEFF(3,1)=2.0D0/9.0D0
COEFF(4,1)=3.0D0/7.0D0
COEFF(5,1)=3.0D0/5.0D0
COEFF(6,1)=4.0D0/5.0D0
COEFF(7,1)=1.0D0
COEFF(8,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/10.0D0
COEFF(3,2)=-2.0D0/81.0D0
COEFF(4,2)=615.0D0/1372.0D0
COEFF(5,2)=3243.0D0/5500.0D0
COEFF(6,2)=-26492.0D0/37125.0D0
COEFF(7,2)=5561.0D0/2376.0D0
COEFF(8,2)=465467.0D0/266112.0D0
COEFF(3,3)=20.0D0/81.0D0
COEFF(4,3)=-270.0D0/343.0D0
COEFF(5,3)=-54.0D0/55.0D0
COEFF(6,3)=72.0D0/55.0D0
COEFF(7,3)=-35.0D0/11.0D0
COEFF(8,3)=-2945.0D0/1232.0D0
COEFF(4,4)=1053.0D0/1372.0D0
COEFF(5,4)=50949.0D0/71500.0D0
COEFF(6,4)=2808.0D0/23375.0D0
COEFF(7,4)=-24117.0D0/31603.0D0
COEFF(8,4)=-561.0201D4/1415.8144D4
COEFF(5,5)=4998.0D0/17875.0D0
COEFF(6,5)=-24206.0D0/37125.0D0
COEFF(7,5)=899983.0D0/200772.0D0
COEFF(8,5)=1051.3573D4/321.2352D4
COEFF(6,6)=338.0D0/459.0D0
COEFF(7,6)=-5225.0D0/1836.0D0
COEFF(8,6)=-424325.0D0/205632.0D0
COEFF(7,7)=3925.0D0/4056.0D0
COEFF(8,7)=376225.0D0/454272.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=61.0D0/864.0D0
COEFF(2,5)=98415.0D0/321776.0D0
COEFF(2,6)=16807.0D0/146016.0D0
COEFF(2,7)=1375.0D0/7344.0D0
COEFF(2,8)=1375.0D0/5408.0D0
COEFF(3,4)=-37.0D0/1120.0D0
COEFF(3,5)=1.0D0/10.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=821.0D0/10800.0D0
COEFF(1,3)=19683.0D0/71825.0D0
COEFF(1,4)=175273.0D0/912600.0D0
COEFF(1,5)=395.0D0/3672.0D0
COEFF(1,6)=785.0D0/2704.0D0
COEFF(1,7)=3.0D0/50.0D0
RETURN
END
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