stode.f

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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 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM,
     1   mxstep, mxhnil, nhnil, ntrep, nslast, cnyh,
     2   ialth, ipup, lmax, meo, nqnyh, nslp
      INTEGER ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, MITER,
     1   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,
     2   illin, init, lyh, lewt, lacor, lsavf, lwm, liwm,
     3   mxstep, mxhnil, nhnil, ntrep, nslast, cnyh,
     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 OCCURRED.
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