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stode.f
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1995-12-14
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SUBROUTINE STODE (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR,
1 WM, IWM, F, JAC, PJAC, SLVS, IERR)
CLLL. OPTIMIZE
EXTERNAL F, JAC, PJAC, SLVS
INTEGER NEQ, NYH, IWM
INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP,
1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER,
2 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU
INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ
DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM
DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO,
2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND
DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP,
1 R, RH, RHDN, RHSM, RHUP, TOLD, VNORM
DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*),
1 ACOR(*), WM(*), IWM(*)
COMMON /LS0001/ CONIT, CRATE, EL(13), ELCO(13,12),
1 HOLD, RMAX, TESCO(3,12),
2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, IOWND(14),
3 IALTH, IPUP, LMAX, MEO, NQNYH, NSLP,
4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER,
5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU
C-----------------------------------------------------------------------
C STODE PERFORMS ONE STEP OF THE INTEGRATION OF AN INITIAL VALUE
C PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.
C NOTE.. STODE IS INDEPENDENT OF THE VALUE OF THE ITERATION METHOD
C INDICATOR MITER, WHEN THIS IS .NE. 0, AND HENCE IS INDEPENDENT
C OF THE TYPE OF CHORD METHOD USED, OR THE JACOBIAN STRUCTURE.
C COMMUNICATION WITH STODE IS DONE WITH THE FOLLOWING VARIABLES..
C
C NEQ = INTEGER ARRAY CONTAINING PROBLEM SIZE IN NEQ(1), AND
C PASSED AS THE NEQ ARGUMENT IN ALL CALLS TO F AND JAC.
C Y = AN ARRAY OF LENGTH .GE. N USED AS THE Y ARGUMENT IN
C ALL CALLS TO F AND JAC.
C YH = AN NYH BY LMAX ARRAY CONTAINING THE DEPENDENT VARIABLES
C AND THEIR APPROXIMATE SCALED DERIVATIVES, WHERE
C LMAX = MAXORD + 1. YH(I,J+1) CONTAINS THE APPROXIMATE
C J-TH DERIVATIVE OF Y(I), SCALED BY H**J/FACTORIAL(J)
C (J = 0,1,...,NQ). ON ENTRY FOR THE FIRST STEP, THE FIRST
C TWO COLUMNS OF YH MUST BE SET FROM THE INITIAL VALUES.
C NYH = A CONSTANT INTEGER .GE. N, THE FIRST DIMENSION OF YH.
C YH1 = A ONE-DIMENSIONAL ARRAY OCCUPYING THE SAME SPACE AS YH.
C EWT = AN ARRAY OF LENGTH N CONTAINING MULTIPLICATIVE WEIGHTS
C FOR LOCAL ERROR MEASUREMENTS. LOCAL ERRORS IN Y(I) ARE
C COMPARED TO 1.0/EWT(I) IN VARIOUS ERROR TESTS.
C SAVF = AN ARRAY OF WORKING STORAGE, OF LENGTH N.
C ALSO USED FOR INPUT OF YH(*,MAXORD+2) WHEN JSTART = -1
C AND MAXORD .LT. THE CURRENT ORDER NQ.
C ACOR = A WORK ARRAY OF LENGTH N, USED FOR THE ACCUMULATED
C CORRECTIONS. ON A SUCCESSFUL RETURN, ACOR(I) CONTAINS
C THE ESTIMATED ONE-STEP LOCAL ERROR IN Y(I).
C WM,IWM = REAL AND INTEGER WORK ARRAYS ASSOCIATED WITH MATRIX
C OPERATIONS IN CHORD ITERATION (MITER .NE. 0).
C PJAC = NAME OF ROUTINE TO EVALUATE AND PREPROCESS JACOBIAN MATRIX
C AND P = I - H*EL0*JAC, IF A CHORD METHOD IS BEING USED.
C SLVS = NAME OF ROUTINE TO SOLVE LINEAR SYSTEM IN CHORD ITERATION.
C CCMAX = MAXIMUM RELATIVE CHANGE IN H*EL0 BEFORE PJAC IS CALLED.
C H = THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP.
C H IS ALTERED BY THE ERROR CONTROL ALGORITHM DURING THE
C PROBLEM. H CAN BE EITHER POSITIVE OR NEGATIVE, BUT ITS
C SIGN MUST REMAIN CONSTANT THROUGHOUT THE PROBLEM.
C HMIN = THE MINIMUM ABSOLUTE VALUE OF THE STEP SIZE H TO BE USED.
C HMXI = INVERSE OF THE MAXIMUM ABSOLUTE VALUE OF H TO BE USED.
C HMXI = 0.0 IS ALLOWED AND CORRESPONDS TO AN INFINITE HMAX.
C HMIN AND HMXI MAY BE CHANGED AT ANY TIME, BUT WILL NOT
C TAKE EFFECT UNTIL THE NEXT CHANGE OF H IS CONSIDERED.
C TN = THE INDEPENDENT VARIABLE. TN IS UPDATED ON EACH STEP TAKEN.
C JSTART = AN INTEGER USED FOR INPUT ONLY, WITH THE FOLLOWING
C VALUES AND MEANINGS..
C 0 PERFORM THE FIRST STEP.
C .GT.0 TAKE A NEW STEP CONTINUING FROM THE LAST.
C -1 TAKE THE NEXT STEP WITH A NEW VALUE OF H, MAXORD,
C N, METH, MITER, AND/OR MATRIX PARAMETERS.
C -2 TAKE THE NEXT STEP WITH A NEW VALUE OF H,
C BUT WITH OTHER INPUTS UNCHANGED.
C ON RETURN, JSTART IS SET TO 1 TO FACILITATE CONTINUATION.
C KFLAG = A COMPLETION CODE WITH THE FOLLOWING MEANINGS..
C 0 THE STEP WAS SUCCESFUL.
C -1 THE REQUESTED ERROR COULD NOT BE ACHIEVED.
C -2 CORRECTOR CONVERGENCE COULD NOT BE ACHIEVED.
C -3 FATAL ERROR IN PJAC OR SLVS.
C A RETURN WITH KFLAG = -1 OR -2 MEANS EITHER
C ABS(H) = HMIN OR 10 CONSECUTIVE FAILURES OCCURRED.
C ON A RETURN WITH KFLAG NEGATIVE, THE VALUES OF TN AND
C THE YH ARRAY ARE AS OF THE BEGINNING OF THE LAST
C STEP, AND H IS THE LAST STEP SIZE ATTEMPTED.
C MAXORD = THE MAXIMUM ORDER OF INTEGRATION METHOD TO BE ALLOWED.
C MAXCOR = THE MAXIMUM NUMBER OF CORRECTOR ITERATIONS ALLOWED.
C MSBP = MAXIMUM NUMBER OF STEPS BETWEEN PJAC CALLS (MITER .GT. 0).
C MXNCF = MAXIMUM NUMBER OF CONVERGENCE FAILURES ALLOWED.
C METH/MITER = THE METHOD FLAGS. SEE DESCRIPTION IN DRIVER.
C N = THE NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS.
C IERR = ERROR FLAG FROM USER-SUPPLIED FUNCTION
C-----------------------------------------------------------------------
KFLAG = 0
TOLD = TN
NCF = 0
IERPJ = 0
IERSL = 0
JCUR = 0
ICF = 0
DELP = 0.0D0
IF (JSTART .GT. 0) GO TO 200
IF (JSTART .EQ. -1) GO TO 100
IF (JSTART .EQ. -2) GO TO 160
C-----------------------------------------------------------------------
C ON THE FIRST CALL, THE ORDER IS SET TO 1, AND OTHER VARIABLES ARE
C INITIALIZED. RMAX IS THE MAXIMUM RATIO BY WHICH H CAN BE INCREASED
C IN A SINGLE STEP. IT IS INITIALLY 1.E4 TO COMPENSATE FOR THE SMALL
C INITIAL H, BUT THEN IS NORMALLY EQUAL TO 10. IF A FAILURE
C OCCURS (IN CORRECTOR CONVERGENCE OR ERROR TEST), RMAX IS SET AT 2
C FOR THE NEXT INCREASE.
C-----------------------------------------------------------------------
LMAX = MAXORD + 1
NQ = 1
L = 2
IALTH = 2
RMAX = 10000.0D0
RC = 0.0D0
EL0 = 1.0D0
CRATE = 0.7D0
HOLD = H
MEO = METH
NSLP = 0
IPUP = MITER
IRET = 3
GO TO 140
C-----------------------------------------------------------------------
C THE FOLLOWING BLOCK HANDLES PRELIMINARIES NEEDED WHEN JSTART = -1.
C IPUP IS SET TO MITER TO FORCE A MATRIX UPDATE.
C IF AN ORDER INCREASE IS ABOUT TO BE CONSIDERED (IALTH = 1),
C IALTH IS RESET TO 2 TO POSTPONE CONSIDERATION ONE MORE STEP.
C IF THE CALLER HAS CHANGED METH, CFODE IS CALLED TO RESET
C THE COEFFICIENTS OF THE METHOD.
C IF THE CALLER HAS CHANGED MAXORD TO A VALUE LESS THAN THE CURRENT
C ORDER NQ, NQ IS REDUCED TO MAXORD, AND A NEW H CHOSEN ACCORDINGLY.
C IF H IS TO BE CHANGED, YH MUST BE RESCALED.
C IF H OR METH IS BEING CHANGED, IALTH IS RESET TO L = NQ + 1
C TO PREVENT FURTHER CHANGES IN H FOR THAT MANY STEPS.
C-----------------------------------------------------------------------
100 IPUP = MITER
LMAX = MAXORD + 1
IF (IALTH .EQ. 1) IALTH = 2
IF (METH .EQ. MEO) GO TO 110
CALL CFODE (METH, ELCO, TESCO)
MEO = METH
IF (NQ .GT. MAXORD) GO TO 120
IALTH = L
IRET = 1
GO TO 150
110 IF (NQ .LE. MAXORD) GO TO 160
120 NQ = MAXORD
L = LMAX
DO 125 I = 1,L
125 EL(I) = ELCO(I,NQ)
NQNYH = NQ*NYH
RC = RC*EL(1)/EL0
EL0 = EL(1)
CONIT = 0.5D0/DBLE(NQ+2)
DDN = VNORM (N, SAVF, EWT)/TESCO(1,L)
EXDN = 1.0D0/DBLE(L)
RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0)
RH = DMIN1(RHDN,1.0D0)
IREDO = 3
IF (H .EQ. HOLD) GO TO 170
RH = DMIN1(RH,DABS(H/HOLD))
H = HOLD
GO TO 175
C-----------------------------------------------------------------------
C CFODE IS CALLED TO GET ALL THE INTEGRATION COEFFICIENTS FOR THE
C CURRENT METH. THEN THE EL VECTOR AND RELATED CONSTANTS ARE RESET
C WHENEVER THE ORDER NQ IS CHANGED, OR AT THE START OF THE PROBLEM.
C-----------------------------------------------------------------------
140 CALL CFODE (METH, ELCO, TESCO)
150 DO 155 I = 1,L
155 EL(I) = ELCO(I,NQ)
NQNYH = NQ*NYH
RC = RC*EL(1)/EL0
EL0 = EL(1)
CONIT = 0.5D0/DBLE(NQ+2)
GO TO (160, 170, 200), IRET
C-----------------------------------------------------------------------
C IF H IS BEING CHANGED, THE H RATIO RH IS CHECKED AGAINST
C RMAX, HMIN, AND HMXI, AND THE YH ARRAY RESCALED. IALTH IS SET TO
C L = NQ + 1 TO PREVENT A CHANGE OF H FOR THAT MANY STEPS, UNLESS
C FORCED BY A CONVERGENCE OR ERROR TEST FAILURE.
C-----------------------------------------------------------------------
160 IF (H .EQ. HOLD) GO TO 200
RH = H/HOLD
H = HOLD
IREDO = 3
GO TO 175
170 RH = DMAX1(RH,HMIN/DABS(H))
175 RH = DMIN1(RH,RMAX)
RH = RH/DMAX1(1.0D0,DABS(H)*HMXI*RH)
R = 1.0D0
DO 180 J = 2,L
R = R*RH
DO 180 I = 1,N
180 YH(I,J) = YH(I,J)*R
H = H*RH
RC = RC*RH
IALTH = L
IF (IREDO .EQ. 0) GO TO 690
C-----------------------------------------------------------------------
C THIS SECTION COMPUTES THE PREDICTED VALUES BY EFFECTIVELY
C MULTIPLYING THE YH ARRAY BY THE PASCAL TRIANGLE MATRIX.
C RC IS THE RATIO OF NEW TO OLD VALUES OF THE COEFFICIENT H*EL(1).
C WHEN RC DIFFERS FROM 1 BY MORE THAN CCMAX, IPUP IS SET TO MITER
C TO FORCE PJAC TO BE CALLED, IF A JACOBIAN IS INVOLVED.
C IN ANY CASE, PJAC IS CALLED AT LEAST EVERY MSBP STEPS.
C-----------------------------------------------------------------------
200 IF (DABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER
IF (NST .GE. NSLP+MSBP) IPUP = MITER
TN = TN + H
I1 = NQNYH + 1
DO 215 JB = 1,NQ
I1 = I1 - NYH
CDIR$ IVDEP
DO 210 I = I1,NQNYH
210 YH1(I) = YH1(I) + YH1(I+NYH)
215 CONTINUE
C-----------------------------------------------------------------------
C UP TO MAXCOR CORRECTOR ITERATIONS ARE TAKEN. A CONVERGENCE TEST IS
C MADE ON THE R.M.S. NORM OF EACH CORRECTION, WEIGHTED BY THE ERROR
C WEIGHT VECTOR EWT. THE SUM OF THE CORRECTIONS IS ACCUMULATED IN THE
C VECTOR ACOR(I). THE YH ARRAY IS NOT ALTERED IN THE CORRECTOR LOOP.
C-----------------------------------------------------------------------
220 M = 0
DO 230 I = 1,N
230 Y(I) = YH(I,1)
IERR = 0
CALL F (NEQ, TN, Y, SAVF, IERR)
IF (IERR .LT. 0) RETURN
NFE = NFE + 1
IF (IPUP .LE. 0) GO TO 250
C-----------------------------------------------------------------------
C IF INDICATED, THE MATRIX P = I - H*EL(1)*J IS REEVALUATED AND
C PREPROCESSED BEFORE STARTING THE CORRECTOR ITERATION. IPUP IS SET
C TO 0 AS AN INDICATOR THAT THIS HAS BEEN DONE.
C-----------------------------------------------------------------------
IERR = 0
CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC,
1 IERR)
IF (IERR .LT. 0) RETURN
IPUP = 0
RC = 1.0D0
NSLP = NST
CRATE = 0.7D0
IF (IERPJ .NE. 0) GO TO 430
250 DO 260 I = 1,N
260 ACOR(I) = 0.0D0
270 IF (MITER .NE. 0) GO TO 350
C-----------------------------------------------------------------------
C IN THE CASE OF FUNCTIONAL ITERATION, UPDATE Y DIRECTLY FROM
C THE RESULT OF THE LAST FUNCTION EVALUATION.
C-----------------------------------------------------------------------
DO 290 I = 1,N
SAVF(I) = H*SAVF(I) - YH(I,2)
290 Y(I) = SAVF(I) - ACOR(I)
DEL = VNORM (N, Y, EWT)
DO 300 I = 1,N
Y(I) = YH(I,1) + EL(1)*SAVF(I)
300 ACOR(I) = SAVF(I)
GO TO 400
C-----------------------------------------------------------------------
C IN THE CASE OF THE CHORD METHOD, COMPUTE THE CORRECTOR ERROR,
C AND SOLVE THE LINEAR SYSTEM WITH THAT AS RIGHT-HAND SIDE AND
C P AS COEFFICIENT MATRIX.
C-----------------------------------------------------------------------
350 DO 360 I = 1,N
360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I))
CALL SLVS (WM, IWM, Y, SAVF)
IF (IERSL .LT. 0) GO TO 430
IF (IERSL .GT. 0) GO TO 410
DEL = VNORM (N, Y, EWT)
DO 380 I = 1,N
ACOR(I) = ACOR(I) + Y(I)
380 Y(I) = YH(I,1) + EL(1)*ACOR(I)
C-----------------------------------------------------------------------
C TEST FOR CONVERGENCE. IF M.GT.0, AN ESTIMATE OF THE CONVERGENCE
C RATE CONSTANT IS STORED IN CRATE, AND THIS IS USED IN THE TEST.
C-----------------------------------------------------------------------
400 IF (M .NE. 0) CRATE = DMAX1(0.2D0*CRATE,DEL/DELP)
DCON = DEL*DMIN1(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT)
IF (DCON .LE. 1.0D0) GO TO 450
M = M + 1
IF (M .EQ. MAXCOR) GO TO 410
IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410
DELP = DEL
IERR = 0
CALL F (NEQ, TN, Y, SAVF, IERR)
IF (IERR .LT. 0) RETURN
NFE = NFE + 1
GO TO 270
C-----------------------------------------------------------------------
C THE CORRECTOR ITERATION FAILED TO CONVERGE.
C IF MITER .NE. 0 AND THE JACOBIAN IS OUT OF DATE, PJAC IS CALLED FOR
C THE NEXT TRY. OTHERWISE THE YH ARRAY IS RETRACTED TO ITS VALUES
C BEFORE PREDICTION, AND H IS REDUCED, IF POSSIBLE. IF H CANNOT BE
C REDUCED OR MXNCF FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -2.
C-----------------------------------------------------------------------
410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430
ICF = 1
IPUP = MITER
GO TO 220
430 ICF = 2
NCF = NCF + 1
RMAX = 2.0D0
TN = TOLD
I1 = NQNYH + 1
DO 445 JB = 1,NQ
I1 = I1 - NYH
CDIR$ IVDEP
DO 440 I = I1,NQNYH
440 YH1(I) = YH1(I) - YH1(I+NYH)
445 CONTINUE
IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680
IF (DABS(H) .LE. HMIN*1.00001D0) GO TO 670
IF (NCF .EQ. MXNCF) GO TO 670
RH = 0.25D0
IPUP = MITER
IREDO = 1
GO TO 170
C-----------------------------------------------------------------------
C THE CORRECTOR HAS CONVERGED. JCUR IS SET TO 0
C TO SIGNAL THAT THE JACOBIAN INVOLVED MAY NEED UPDATING LATER.
C THE LOCAL ERROR TEST IS MADE AND CONTROL PASSES TO STATEMENT 500
C IF IT FAILS.
C-----------------------------------------------------------------------
450 JCUR = 0
IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ)
IF (M .GT. 0) DSM = VNORM (N, ACOR, EWT)/TESCO(2,NQ)
IF (DSM .GT. 1.0D0) GO TO 500
C-----------------------------------------------------------------------
C AFTER A SUCCESSFUL STEP, UPDATE THE YH ARRAY.
C CONSIDER CHANGING H IF IALTH = 1. OTHERWISE DECREASE IALTH BY 1.
C IF IALTH IS THEN 1 AND NQ .LT. MAXORD, THEN ACOR IS SAVED FOR
C USE IN A POSSIBLE ORDER INCREASE ON THE NEXT STEP.
C IF A CHANGE IN H IS CONSIDERED, AN INCREASE OR DECREASE IN ORDER
C BY ONE IS CONSIDERED ALSO. A CHANGE IN H IS MADE ONLY IF IT IS BY A
C FACTOR OF AT LEAST 1.1. IF NOT, IALTH IS SET TO 3 TO PREVENT
C TESTING FOR THAT MANY STEPS.
C-----------------------------------------------------------------------
KFLAG = 0
IREDO = 0
NST = NST + 1
HU = H
NQU = NQ
DO 470 J = 1,L
DO 470 I = 1,N
470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I)
IALTH = IALTH - 1
IF (IALTH .EQ. 0) GO TO 520
IF (IALTH .GT. 1) GO TO 700
IF (L .EQ. LMAX) GO TO 700
DO 490 I = 1,N
490 YH(I,LMAX) = ACOR(I)
GO TO 700
C-----------------------------------------------------------------------
C THE ERROR TEST FAILED. KFLAG KEEPS TRACK OF MULTIPLE FAILURES.
C RESTORE TN AND THE YH ARRAY TO THEIR PREVIOUS VALUES, AND PREPARE
C TO TRY THE STEP AGAIN. COMPUTE THE OPTIMUM STEP SIZE FOR THIS OR
C ONE LOWER ORDER. AFTER 2 OR MORE FAILURES, H IS FORCED TO DECREASE
C BY A FACTOR OF 0.2 OR LESS.
C-----------------------------------------------------------------------
500 KFLAG = KFLAG - 1
TN = TOLD
I1 = NQNYH + 1
DO 515 JB = 1,NQ
I1 = I1 - NYH
CDIR$ IVDEP
DO 510 I = I1,NQNYH
510 YH1(I) = YH1(I) - YH1(I+NYH)
515 CONTINUE
RMAX = 2.0D0
IF (DABS(H) .LE. HMIN*1.00001D0) GO TO 660
IF (KFLAG .LE. -3) GO TO 640
IREDO = 2
RHUP = 0.0D0
GO TO 540
C-----------------------------------------------------------------------
C REGARDLESS OF THE SUCCESS OR FAILURE OF THE STEP, FACTORS
C RHDN, RHSM, AND RHUP ARE COMPUTED, BY WHICH H COULD BE MULTIPLIED
C AT ORDER NQ - 1, ORDER NQ, OR ORDER NQ + 1, RESPECTIVELY.
C IN THE CASE OF FAILURE, RHUP = 0.0 TO AVOID AN ORDER INCREASE.
C THE LARGEST OF THESE IS DETERMINED AND THE NEW ORDER CHOSEN
C ACCORDINGLY. IF THE ORDER IS TO BE INCREASED, WE COMPUTE ONE
C ADDITIONAL SCALED DERIVATIVE.
C-----------------------------------------------------------------------
520 RHUP = 0.0D0
IF (L .EQ. LMAX) GO TO 540
DO 530 I = 1,N
530 SAVF(I) = ACOR(I) - YH(I,LMAX)
DUP = VNORM (N, SAVF, EWT)/TESCO(3,NQ)
EXUP = 1.0D0/DBLE(L+1)
RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0)
540 EXSM = 1.0D0/DBLE(L)
RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0)
RHDN = 0.0D0
IF (NQ .EQ. 1) GO TO 560
DDN = VNORM (N, YH(1,L), EWT)/TESCO(1,NQ)
EXDN = 1.0D0/DBLE(NQ)
RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0)
560 IF (RHSM .GE. RHUP) GO TO 570
IF (RHUP .GT. RHDN) GO TO 590
GO TO 580
570 IF (RHSM .LT. RHDN) GO TO 580
NEWQ = NQ
RH = RHSM
GO TO 620
580 NEWQ = NQ - 1
RH = RHDN
IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0
GO TO 620
590 NEWQ = L
RH = RHUP
IF (RH .LT. 1.1D0) GO TO 610
R = EL(L)/DBLE(L)
DO 600 I = 1,N
600 YH(I,NEWQ+1) = ACOR(I)*R
GO TO 630
610 IALTH = 3
GO TO 700
620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610
IF (KFLAG .LE. -2) RH = DMIN1(RH,0.2D0)
C-----------------------------------------------------------------------
C IF THERE IS A CHANGE OF ORDER, RESET NQ, L, AND THE COEFFICIENTS.
C IN ANY CASE H IS RESET ACCORDING TO RH AND THE YH ARRAY IS RESCALED.
C THEN EXIT FROM 690 IF THE STEP WAS OK, OR REDO THE STEP OTHERWISE.
C-----------------------------------------------------------------------
IF (NEWQ .EQ. NQ) GO TO 170
630 NQ = NEWQ
L = NQ + 1
IRET = 2
GO TO 150
C-----------------------------------------------------------------------
C CONTROL REACHES THIS SECTION IF 3 OR MORE FAILURES HAVE OCCURED.
C IF 10 FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -1.
C IT IS ASSUMED THAT THE DERIVATIVES THAT HAVE ACCUMULATED IN THE
C YH ARRAY HAVE ERRORS OF THE WRONG ORDER. HENCE THE FIRST
C DERIVATIVE IS RECOMPUTED, AND THE ORDER IS SET TO 1. THEN
C H IS REDUCED BY A FACTOR OF 10, AND THE STEP IS RETRIED,
C UNTIL IT SUCCEEDS OR H REACHES HMIN.
C-----------------------------------------------------------------------
640 IF (KFLAG .EQ. -10) GO TO 660
RH = 0.1D0
RH = DMAX1(HMIN/DABS(H),RH)
H = H*RH
DO 645 I = 1,N
645 Y(I) = YH(I,1)
IERR = 0
CALL F (NEQ, TN, Y, SAVF, IERR)
IF (IERR .LT. 0) RETURN
NFE = NFE + 1
DO 650 I = 1,N
650 YH(I,2) = H*SAVF(I)
IPUP = MITER
IALTH = 5
IF (NQ .EQ. 1) GO TO 200
NQ = 1
L = 2
IRET = 3
GO TO 150
C-----------------------------------------------------------------------
C ALL RETURNS ARE MADE THROUGH THIS SECTION. H IS SAVED IN HOLD
C TO ALLOW THE CALLER TO CHANGE H ON THE NEXT STEP.
C-----------------------------------------------------------------------
660 KFLAG = -1
GO TO 720
670 KFLAG = -2
GO TO 720
680 KFLAG = -3
GO TO 720
690 RMAX = 10.0D0
700 R = 1.0D0/TESCO(2,NQU)
DO 710 I = 1,N
710 ACOR(I) = ACOR(I)*R
720 HOLD = H
JSTART = 1
RETURN
C----------------------- END OF SUBROUTINE STODE -----------------------
END