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SUBROUTINE RKE54 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKE5(4) (method of England). *
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 : G. Engeln-Müllges F. Reuter : *
C Formelsammlung zur Numerischen Mathematik mit *
C Standard FORTRAN 77 - Programmen *
C page 334 *
C Wissenschaftsverlag 1988 *
C *
C*****************************************************************
C
C Declarations
C
DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
QG=4.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme )
C
COEFF(2,1)=1.0D0/2.0D0
COEFF(3,1)=1.0D0/2.0D0
COEFF(4,1)=1.0D0
COEFF(5,1)=2.0D0/3.0D0
COEFF(6,1)=1.0D0/5.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/2.0D0
COEFF(3,2)=1.0D0/4.0D0
COEFF(5,2)=7.0D0/27.0D0
COEFF(6,2)=28.0D0/625.0D0
COEFF(3,3)=1.0D0/4.0D0
COEFF(4,3)=-1.0D0
COEFF(5,3)=10.0D0/27.0D0
COEFF(6,3)=-125.0D0/625.0D0
COEFF(4,4)=2.0D0
COEFF(6,4)=546.0D0/625.0D0
COEFF(5,5)=1.0D0/27.0D0
COEFF(6,5)=54.0D0/625.0D0
COEFF(6,6)=-378.0D0/625.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=14.0D0/336.0D0
COEFF(2,6)=35.0D0/336.0D0
COEFF(3,4)=162.0D0/336.0D0
COEFF(3,5)=125.0D0/336.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=1.0D0/6.0D0
COEFF(1,3)=4.0D0/6.0D0
COEFF(1,4)=1.0D0/6.0D0
RETURN
END
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