SLATEC Routines --- INTYD ---

```*DECK INTYD
SUBROUTINE INTYD (T, K, YH, NYH, DKY, IFLAG)
C***BEGIN PROLOGUE  INTYD
C***SUBSIDIARY
C***PURPOSE  Subsidiary to DEBDF
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (INTYD-S, DINTYD-D)
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   INTYD approximates the solution and derivatives at T by polynomial
C   interpolation. Must be used in conjunction with the integrator
C   package DEBDF.
C ----------------------------------------------------------------------
C INTYD computes interpolated values of the K-th derivative of the
C dependent variable vector Y, and stores it in DKY.
C This routine is called by DEBDF with K = 0,1 and T = TOUT, but may
C also be called by the user for any K up to the current order.
C (see detailed instructions in LSODE usage documentation.)
C ----------------------------------------------------------------------
C The computed values in DKY are gotten by interpolation using the
C Nordsieck history array YH.  This array corresponds uniquely to a
C vector-valued polynomial of degree NQCUR or less, and DKY is set
C to the K-th derivative of this polynomial at T.
C The formula for DKY is..
C              Q
C  DKY(I)  =  sum  C(J,K) * (T - TN)**(J-K) * H**(-J) * YH(I,J+1)
C             J=K
C where  C(J,K) = J*(J-1)*...*(J-K+1), Q = NQCUR, TN = TCUR, H = HCUR.
C The quantities  NQ = NQCUR, L = NQ+1, N = NEQ, TN, and H are
C communicated by common.  The above sum is done in reverse order.
C IFLAG is returned negative if either K or T is out of bounds.
C ----------------------------------------------------------------------
C