C      ALGORITHM 688, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 17, NO. 2, PP. 153-166.  JUNE, 1991.
C       The programs on the tape are as follows :
C
C       1. README   This file.
C
C       2. ex1drvsp.f  A single precision driving routine for example 1
C       of Sincovec and Madsen. Includes the subroutines :
C
C      MAIN
C      SUBROUTINE F(T,X,U,UX,UXX,FVAL,NPDE)
C      SUBROUTINE BNDRY(T,X,U,UX,DBDU,DBDUX,DZDT,NPDE)
C      SUBROUTINE UINIT(X,U,NPDE)
C      SUBROUTINE DERIVF(T,X,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE)
C
C       3. ex2drvsp.f  A single precision driving routine for example 2
C       of Sincovec and Madsen. Includes the subroutines.
C
C      MAIN
C      SUBROUTINE F(T,X,U,UX,UXX,FVAL,NPDE)
C      SUBROUTINE BNDRY(T,X,U,UX,DBDU,DBDUX,DZDT,NPDE)
C      SUBROUTINE UINIT(X,U,NPDE)
C      SUBROUTINE DERIVF(T,X,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE)
C      REAL FUNCTION EXACTV(X,T)
C
C       4. pdecolsp.f  The single precision version of the modified pdecol.
C
C       The subroutines are in the following order : (only the eight routines
C       above the line of asterisks differ from the original code, with
C       CRDCMP and CRSLVE replacing DECB and SOLB.
C
C      SUBROUTINE PDECOL(T0,TOUT,DT,XBKPT,EPS,NINT,KORD,NCC,NPDE,MF,
C      SUBROUTINE ADDA(PW,A,BC,NPDE)
C      SUBROUTINE DIFFUN (N, T, Y, YDOT, IFLAG, PW, IPIV, WORK, IWORK)
C      SUBROUTINE INITAL(K,A,RHS,X,XT,XC,PW,IPIV,ILEFT)
C      SUBROUTINE PSETIB (C, PW, N0, CON, MITER, IFLAG, A, ILEFT, XC,
C      SUBROUTINE STIFIB (N0,Y,YMAX,ERROR,SAVE1,SAVE2,SAVE3,
C      SUBROUTINE CRDCMP(N,TOPBLK,NRWTOP,NOVRLP,ARRAY,NRWBLK,
C      SUBROUTINE CRSLVE(TOPBLK,NRWTOP,NOVRLP,ARRAY,NRWBLK,
C
C     **************************************************************
C
C      SUBROUTINE BSPLVD ( XT, K, X, ILEFT, VNIKX, NDERIV )
C      SUBROUTINE BSPLVN ( XT, JHIGH, INDEX, X, ILEFT, VNIKX )
C      SUBROUTINE INTERV ( XT, LXT, X, ILEFT, MFLAG )
C      SUBROUTINE COLPNT(X, XC, XT)
C      SUBROUTINE COSET (METH, NQ, EL, TQ)
C      SUBROUTINE DIFFF(T,X,IPT,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE,CMAX,
C      SUBROUTINE EVAL(ICPT,NPDE,C,UVAL,A,ILEFT)
C      SUBROUTINE GFUN (T,C,UDOT,NPDE,NCPTS,A,BC,DBDU,DBDUX,DZDT,
C      SUBROUTINE INTERP (TOUT, Y, N0, Y0)
C      SUBROUTINE RES(T,H,C,V,R,NPDE,NCPTS,A,ILEFT,BC,DBDU,DBDUX,DZDT,
C      SUBROUTINE VALUES(X,USOL,SCTCH,NDIM1,NDIM2,NPTS,NDERV,WORK)
C
C       5. ex1drvdp.f  A double precision driving routine for example 1
C       of Sincovec and Madsen. Includes the subroutines.
C
C      MAIN
C      SUBROUTINE F(T,X,U,UX,UXX,FVAL,NPDE)
C      SUBROUTINE BNDRY(T,X,U,UX,DBDU,DBDUX,DZDT,NPDE)
C      SUBROUTINE UINIT(X,U,NPDE)
C      SUBROUTINE DERIVF(T,X,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE)
C
C       6. ex2drvdp.f  A double precision driving routine for example 2
C       of Sincovec and Madsen. Includes the subroutines.
C
C      MAIN
C      SUBROUTINE F(T,X,U,UX,UXX,FVAL,NPDE)
C      SUBROUTINE BNDRY(T,X,U,UX,DBDU,DBDUX,DZDT,NPDE)
C      SUBROUTINE UINIT(X,U,NPDE)
C      SUBROUTINE DERIVF(T,X,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE)
C      DOUBLE PRECISION FUNCTION EXACTV(X,T)
C
C
C       7. pdecoldp.f  The double precision version of the modified pdecol.
C
C       The subroutines are in the following order : (only the eight routines
C       above the line of asterisks differ from the original code, with
C       CRDCMP and CRSLVE replacing DECB and SOLB.
C
C      SUBROUTINE PDECOL(T0,TOUT,DT,XBKPT,EPS,NINT,KORD,NCC,NPDE,MF,
C      SUBROUTINE ADDA(PW,A,BC,NPDE)
C      SUBROUTINE DIFFUN (N, T, Y, YDOT, IFLAG, PW, IPIV, WORK, IWORK)
C      SUBROUTINE INITAL(K,A,RHS,X,XT,XC,PW,IPIV,ILEFT)
C      SUBROUTINE PSETIB (C, PW, N0, CON, MITER, IFLAG, A, ILEFT, XC,
C      SUBROUTINE STIFIB (N0,Y,YMAX,ERROR,SAVE1,SAVE2,SAVE3,
C      SUBROUTINE CRDCMP(N,TOPBLK,NRWTOP,NOVRLP,ARRAY,NRWBLK,
C      SUBROUTINE CRSLVE(TOPBLK,NRWTOP,NOVRLP,ARRAY,NRWBLK,
C
C      **************************************************************
C
C      SUBROUTINE BSPLVD ( XT, K, X, ILEFT, VNIKX, NDERIV )
C      SUBROUTINE BSPLVN ( XT, JHIGH, INDEX, X, ILEFT, VNIKX )
C      SUBROUTINE INTERV ( XT, LXT, X, ILEFT, MFLAG )
C      SUBROUTINE COLPNT(X, XC, XT)
C      SUBROUTINE COSET (METH, NQ, EL, TQ)
C      SUBROUTINE DIFFF(T,X,IPT,U,UX,UXX,DFDU,DFDUX,DFDUXX,NPDE,CMAX,
C      SUBROUTINE EVAL(ICPT,NPDE,C,UVAL,A,ILEFT)
C      SUBROUTINE GFUN (T,C,UDOT,NPDE,NCPTS,A,BC,DBDU,DBDUX,DZDT,
C      SUBROUTINE INTERP (TOUT, Y, N0, Y0)
C      SUBROUTINE RES(T,H,C,V,R,NPDE,NCPTS,A,ILEFT,BC,DBDU,DBDUX,DZDT,
C      SUBROUTINE VALUES(X,USOL,SCTCH,NDIM1,NDIM2,NPTS,NDERV,WORK)
