*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 C***SEE ALSO DEBDF C***ROUTINES CALLED (NONE) C***COMMON BLOCKS DEBDF1 C***REVISION HISTORY (YYMMDD) C 800901 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 891214 Prologue converted to Version 4.0 format. (BAB) C 900328 Added TYPE section. (WRB) C 910722 Updated AUTHOR section. (ALS) C***END PROLOGUE INTYD