# sintrp.f

          SUBROUTINE SINTRP (X, Y, XOUT, YOUT, YPOUT, NEQN, KOLD, PHI, IVC,
         +   IV, KGI, GI, ALPHA, OG, OW, OX, OY)
    C***BEGIN PROLOGUE  SINTRP
    C***PURPOSE  Approximate the solution at XOUT by evaluating the
    C            polynomial computed in STEPS at XOUT.  Must be used in
    C            conjunction with STEPS.
    C***LIBRARY   SLATEC (DEPAC)
    C***CATEGORY  I1A1B
    C***TYPE      SINGLE PRECISION (SINTRP-S, DINTP-D)
    C***KEYWORDS  ADAMS METHOD, DEPAC, INITIAL VALUE PROBLEMS, ODE,
    C             ORDINARY DIFFERENTIAL EQUATIONS, PREDICTOR-CORRECTOR,
    C             SMOOTH INTERPOLANT
    C***AUTHOR  Watts, H. A., (SNLA)
    C***DESCRIPTION
    C
    C   The methods in subroutine  STEPS  approximate the solution near  X
    C   by a polynomial.  Subroutine  SINTRP  approximates the solution at
    C   XOUT  by evaluating the polynomial there.  Information defining this
    C   polynomial is passed from  STEPS  so  SINTRP  cannot be used alone.
    C
    C   Subroutine STEPS is completely explained and documented in the text,
    C   "Computer Solution of Ordinary Differential Equations, the Initial
    C   Value Problem"  by L. F. Shampine and M. K. Gordon.
    C
    C   Input to SINTRP --
    C
    C   The user provides storage in the calling program for the arrays in
    C   the call list
    C      DIMENSION Y(NEQN),YOUT(NEQN),YPOUT(NEQN),PHI(NEQN,16),OY(NEQN)
    C                AND ALPHA(12),OG(13),OW(12),GI(11),IV(10)
    C   and defines
    C      XOUT -- point at which solution is desired.
    C   The remaining parameters are defined in  STEPS  and passed to
    C   SINTRP  from that subroutine
    C
    C   Output from  SINTRP --
    C
    C      YOUT(*) -- solution at  XOUT
    C      YPOUT(*) -- derivative of solution at  XOUT
    C   The remaining parameters are returned unaltered from their input
    C   values.  Integration with  STEPS  may be continued.
    C
    C***REFERENCES  H. A. Watts, A smoother interpolant for DE/STEP, INTRP
    C                 II, Report SAND84-0293, Sandia Laboratories, 1984.
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   840201  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  SINTRP