*DECK SINTRP
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
C
DIMENSION Y(*),YOUT(*),YPOUT(*),PHI(NEQN,16),OY(*)
DIMENSION G(13),C(13),W(13),OG(13),OW(12),ALPHA(12),GI(11),IV(10)
C
C***FIRST EXECUTABLE STATEMENT SINTRP
KP1 = KOLD + 1
KP2 = KOLD + 2
C
HI = XOUT - OX
H = X - OX
XI = HI/H
XIM1 = XI - 1.
C
C INITIALIZE W(*) FOR COMPUTING G(*)
C
XIQ = XI
DO 10 IQ = 1,KP1
XIQ = XI*XIQ
TEMP1 = IQ*(IQ+1)
10 W(IQ) = XIQ/TEMP1
C
C COMPUTE THE DOUBLE INTEGRAL TERM GDI
C
IF (KOLD .LE. KGI) GO TO 50
IF (IVC .GT. 0) GO TO 20
GDI = 1.0/TEMP1
M = 2
GO TO 30
20 IW = IV(IVC)
GDI = OW(IW)
M = KOLD - IW + 3
30 IF (M .GT. KOLD) GO TO 60
DO 40 I = M,KOLD
40 GDI = OW(KP2-I) - ALPHA(I)*GDI
GO TO 60
50 GDI = GI(KOLD)
C
C COMPUTE G(*) AND C(*)
C
60 G(1) = XI
G(2) = 0.5*XI*XI
C(1) = 1.0
C(2) = XI
IF (KOLD .LT. 2) GO TO 90
DO 80 I = 2,KOLD
ALP = ALPHA(I)
GAMMA = 1.0 + XIM1*ALP
L = KP2 - I
DO 70 JQ = 1,L
70 W(JQ) = GAMMA*W(JQ) - ALP*W(JQ+1)
G(I+1) = W(1)
80 C(I+1) = GAMMA*C(I)
C
C DEFINE INTERPOLATION PARAMETERS
C
90 SIGMA = (W(2) - XIM1*W(1))/GDI
RMU = XIM1*C(KP1)/GDI
HMU = RMU/H
C
C INTERPOLATE FOR THE SOLUTION -- YOUT
C AND FOR THE DERIVATIVE OF THE SOLUTION -- YPOUT
C
DO 100 L = 1,NEQN
YOUT(L) = 0.0
100 YPOUT(L) = 0.0
DO 120 J = 1,KOLD
I = KP2 - J
GDIF = OG(I) - OG(I-1)
TEMP2 = (G(I) - G(I-1)) - SIGMA*GDIF
TEMP3 = (C(I) - C(I-1)) + RMU*GDIF
DO 110 L = 1,NEQN
YOUT(L) = YOUT(L) + TEMP2*PHI(L,I)
110 YPOUT(L) = YPOUT(L) + TEMP3*PHI(L,I)
120 CONTINUE
DO 130 L = 1,NEQN
YOUT(L) = ((1.0 - SIGMA)*OY(L) + SIGMA*Y(L)) +
1 H*(YOUT(L) + (G(1) - SIGMA*OG(1))*PHI(L,1))
130 YPOUT(L) = HMU*(OY(L) - Y(L)) +
1 (YPOUT(L) + (C(1) + RMU*OG(1))*PHI(L,1))
C
RETURN
END