BVSUP

      SUBROUTINE BVSUP(Y,NROWY,NCOMP,XPTS,NXPTS,A,NROWA,ALPHA,NIC,
     1   B,NROWB,BETA,NFC,IGOFX,RE,AE,IFLAG,WORK,NDW,IWORK,NDIW,NEQIVP)
C***BEGIN PROLOGUE  BVSUP
C***DATE WRITTEN   01 JUN 1975
C***REVISION DATE  811015   (YYMMDD)
C***CATEGORY NO.  D2B
C***KEYWORDS  BOUNDARY VALUE,TWO POINT,ORTHONORMALIZATION,SHOOTING
C***AUTHOR  SCOTT, M. R., SNLA
C           WATTS, H. A., SNLA
C***PURPOSE  SUBROUTINE BVSUP SOLVES A LINEAR TWO-POINT BOUNDARY
C            VALUE PROBLEM USING SUPERPOSITION COUPLED WITH AN
C            ORTHONORMALIZATION PROCEDURE AND A VARIABLE-STEP
C            INTEGRATION SCHEME.
C***DESCRIPTION
C
C **********************************************************************
C
C     SUBROUTINE BVSUP SOLVES A LINEAR TWO-POINT BOUNDARY-VALUE PROBLEM
C     OF THE FORM
C                        DY/DX = MATRIX(X,U)*Y(X) + G(X,U)
C                A*Y(XINITIAL) = ALPHA ,  B*Y(XFINAL) = BETA
C
C     COUPLED WITH THE SOLUTION OF THE INITIAL VALUE PROBLEM
C
C                        DU/DX = F(X,U)
C                      U(XINITIAL) = ETA
C
C **********************************************************************
C     ABSTRACT
C        THE METHOD OF SOLUTION USES SUPERPOSITION COUPLED WITH AN
C     ORTHONORMALIZATION PROCEDURE AND A VARIABLE-STEP INTEGRATION
C     SCHEME.  EACH TIME THE SUPERPOSITION SOLUTIONS START TO
C     LOSE THEIR NUMERICAL LINEAR INDEPENDENCE, THE VECTORS ARE
C     REORTHONORMALIZED BEFORE INTEGRATION PROCEEDS.  THE UNDERLYING
C     PRINCIPLE OF THE ALGORITHM IS THEN TO PIECE TOGETHER THE
C     INTERMEDIATE (ORTHOGONALIZED) SOLUTIONS, DEFINED ON THE VARIOUS
C     SUBINTERVALS, TO OBTAIN THE DESIRED SOLUTIONS.
C