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SUBROUTINE HIHA5 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula HIHA5 (method of Higham und Hall). *
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. Hairer G. Wanner : *
C Solving Ordinary Differential Equations II *
C page 28-31 *
C Springer-Verlag Berlin Heidelberg 1991 *
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)=2.0D0/9.0D0
COEFF(3,1)=1.0D0/3.0D0
COEFF(4,1)=1.0D0/2.0D0
COEFF(5,1)=3.0D0/5.0D0
COEFF(6,1)=1.0D0
COEFF(7,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=2.0D0/9.0D0
COEFF(3,2)=1.0D0/12.0D0
COEFF(4,2)=1.0D0/8.0D0
COEFF(5,2)=91.0D0/500.0D0
COEFF(6,2)=-11.0D0/20.0D0
COEFF(7,2)=1.0D0/12.0D0
COEFF(3,3)=1.0D0/4.0D0
COEFF(5,3)=-27.0D0/100.0D0
COEFF(6,3)=27.0D0/20.0D0
COEFF(4,4)=3.0D0/8.0D0
COEFF(5,4)=78.0D0/125.0D0
COEFF(6,4)=12.0D0/5.0D0
COEFF(7,4)=27.0D0/32.0D0
COEFF(5,5)=8.0D0/125.0D0
COEFF(6,5)=-36.0D0/5.0D0
COEFF(7,5)=-4.0D0/3.0D0
COEFF(6,6)=5.0D0
COEFF(7,6)=125.0D0/96.0D0
COEFF(7,7)=5.0D0/48.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=1.0D0/12.0D0
COEFF(2,5)=27.0D0/32.0D0
COEFF(2,6)=-4.0D0/3.0D0
COEFF(2,7)=125.0D0/96.0D0
COEFF(3,4)=5.0D0/48.0D0
C
C A - values (see scheme)
C
\hbox{\JDhspace\verb`
COEFF(1,1)=2.0D0/15.0D0
COEFF(1,3)=27.0D0/80.0D0
COEFF(1,4)=-2.0D0/15.0D0
COEFF(1,5)=25.0D0/48.0D0
COEFF(1,6)=1.0D0/24.0D0
COEFF(1,7)=1.0D0/10.0D0
RETURN
END
Begin of file
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