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SUBROUTINE RK8713 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RK8(7)13M (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=7.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme )
C
COEFF(2,1)=1.0D0/18.0D0
COEFF(3,1)=1.0D0/12.0D0
COEFF(4,1)=1.0D0/8.0D0
COEFF(5,1)=5.0D0/16.0D0
COEFF(6,1)=3.0D0/8.0D0
COEFF(7,1)=59.0D0/400.0D0
COEFF(8,1)=93.0D0/200.0D0
COEFF(9,1)=549002.3248D4/971916.9821D4
COEFF(10,1)=13.0D0/20.0D0
COEFF(11,1)=120114.6811D4/129901.9798D4
COEFF(12,1)=1.0D0
COEFF(13,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/18.0D0
COEFF(3,2)=1.0D0/48.0D0
COEFF(4,2)=1.0D0/32.0D0
COEFF(5,2)=5.0D0/16.0D0
COEFF(6,2)=3.0D0/80.0D0
COEFF(7,2)=2944.3841D4/61456.3906D4
COEFF(8,2)=1601.6141D4/94669.2911D4
COEFF(9,2)=3963.2708D4/57359.1083D4
COEFF(10,2)=24612.1993D4/134084.7787D4
COEFF(11,2)=-102846.8189D4/84618.0014D4
COEFF(12,2)=18589.2177D4/71811.6043D4
COEFF(13,2)=40386.3854D4/49106.3109D4
COEFF(3,3)=1.0D0/16.0D0
COEFF(4,4)=3.0D0/32.0D0
COEFF(5,4)=-75.0D0/64.0D0
COEFF(5,5)=75.0D0/64.0D0
COEFF(6,5)=3.0D0/16.0D0
COEFF(7,5)=7773.6538D4/69253.8347D4
COEFF(8,5)=6156.4180D4/15873.2637D4
COEFF(9,5)=-43363.6366D4/68370.1615D4
COEFF(10,5)=-376950.42795D5/152687.66246D5
COEFF(11,5)=847823.5783D4/50851.2852D4
COEFF(12,5)=-318509.4517D4/66710.7341D4
COEFF(13,5)=-506849.2393D4/43474.0067D4
COEFF(6,6)=3.0D0/20.0D0
COEFF(7,6)=-2869.3883D4/112500.0000D4
COEFF(8,6)=2278.9713D4/63344.5777D4
COEFF(9,6)=-42173.9975D4/261629.2301D4
COEFF(10,6)=-30912.1744D4/106122.7803D4
COEFF(11,6)=131172.9495D4/143242.2823D4
COEFF(12,6)=-47775.5414D4/109805.3517D4
COEFF(13,6)=-41142.1997D4/54304.3805D4
COEFF(7,7)=2312.4283D4/180000.0000D4
COEFF(8,7)=54581.5736D4/277105.7229D4
COEFF(9,7)=10030.2831D4/72342.3059D4
COEFF(10,7)=-1299.2083D4/49076.6935D4
COEFF(11,7)=-103041.29995D5/17013.04382D5
COEFF(12,7)=-70363.5378D4/23073.9211D4
COEFF(13,7)=65278.3627D4/91429.6604D4
COEFF(8,8)=-18019.3667D4/104330.7555D4
COEFF(9,8)=79020.4164D4/83981.3087D4
COEFF(10,8)=600594.3493D4/210894.7869D4
COEFF(11,8)=-487779.25059D5/30479.39560D5
COEFF(12,8)=573156.6787D4/102754.5527D4
COEFF(13,8)=111739.62825D5/9253.20556D5
COEFF(9,9)=80063.5310D4/378307.1287D4
COEFF(10,9)=39300.6217D4/139667.3457D4
COEFF(11,9)=153367.26248D5/10328.24649D5
COEFF(12,9)=523286.6602D4/85006.6563D4
COEFF(13,9)=-131589.90841D5/61847.27034D5
COEFF(10,10)=12387.2331D4/100102.9789D4
COEFF(11,10)=-454428.68181D5/33984.67696D5
COEFF(12,10)=-409366.4535D4/80868.8257D4
COEFF(13,10)=393664.7629D4/197804.9680D4
COEFF(11,11)=306599.3473D4/59717.2653D4
COEFF(12,11)=396213.7247D4/180595.7418D4
COEFF(13,11)=-16052.8059D4/68517.8525D4
COEFF(12,12)=6568.6358D4/48791.0083D4
COEFF(13,12)=24863.8103D4/141353.1060D4
C
C A tilde values (see scheme)
C
COEFF(2,3)=1400.5451D4/33548.0064D4
COEFF(2,8)=-5923.8493D4/106827.7825D4
COEFF(2,9)=18160.6767D4/75886.7731D4
COEFF(2,10)=56129.2985D4/79784.5732D4
COEFF(2,11)=-104189.1430D4/137134.3529D4
COEFF(2,12)=76041.7239D4/115116.5299D4
COEFF(2,13)=11882.0643D4/75113.8087D4
COEFF(3,4)=-52874.7749D4/222060.7170D4
COEFF(3,5)=1.0D0/4.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=1345.1932D4/45517.6623D4
COEFF(1,6)=-80871.9846D4/97600.0145D4
COEFF(1,7)=175700.4468D4/564515.9321D4
COEFF(1,8)=65604.5339D4/26589.1186D4
COEFF(1,9)=-386757.4721D4/151851.7206D4
COEFF(1,10)=46588.5868D4/32273.6535D4
COEFF(1,11)=5301.1238D4/66751.6719D4
COEFF(1,12)=2.0D0/45.0D0
RETURN
END
Begin of file
Contents
Index