*DECK DSTODA
SUBROUTINE DSTODA (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR,
1 WM, IWM, F, JAC, PJAC, SLVS)
EXTERNAL F, JAC, PJAC, SLVS
INTEGER NEQ, NYH, IWM
DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM
DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*),
1 ACOR(*), WM(*), IWM(*)
INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP,
1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L,
2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER,
3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU
INTEGER IOWND2, ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS
DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO,
2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND
DOUBLE PRECISION ROWND2, CM1, CM2, PDEST, PDLAST, RATIO,
1 PDNORM
COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12),
1 HOLD, RMAX, TESCO(3,12),
2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND,
3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP,
4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L,
5 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER,
6 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU
COMMON /DLSA01/ ROWND2, CM1(12), CM2(5), PDEST, PDLAST, RATIO,
1 PDNORM,
2 IOWND2(3), ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS
INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ
INTEGER LM1, LM1P1, LM2, LM2P1, NQM1, NQM2
DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP,
1 R, RH, RHDN, RHSM, RHUP, TOLD, DMNORM
DOUBLE PRECISION ALPHA, DM1,DM2, EXM1,EXM2,
1 PDH, PNORM, RATE, RH1, RH1IT, RH2, RM, SM1(12)
SAVE SM1
DATA SM1/0.5D0, 0.575D0, 0.55D0, 0.45D0, 0.35D0, 0.25D0,
1 0.20D0, 0.15D0, 0.10D0, 0.075D0, 0.050D0, 0.025D0/
C-----------------------------------------------------------------------
C DSTODA performs one step of the integration of an initial value
C problem for a system of ordinary differential equations.
C Note: DSTODA 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 DSTODA is done with the following variables:
C
C Y = an array of length .ge. N used as the Y argument in
C all calls to F and JAC.
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 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 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 It also returns an estimate of norm(Jac) in PDNORM.
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,
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 = current method.
C METH = 1 means Adams method (nonstiff)
C METH = 2 means BDF method (stiff)
C METH may be reset by DSTODA.
C MITER = corrector iteration method.
C MITER = 0 means functional iteration.
C MITER = JT .gt. 0 means a chord iteration corresponding
C to Jacobian type JT. (The DLSODA/DLSODAR argument JT is
C communicated here as JTYP, but is not used in DSTODA
C except to load MITER following a method switch.)
C MITER may be reset by DSTODA.
C N = the number of first-order differential equations.
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 DCFODE is called to get the needed coefficients for both methods.
C-----------------------------------------------------------------------
LMAX = MAXORD + 1
NQ = 1
L = 2
IALTH = 2
RMAX = 10000.0D0
RC = 0.0D0
EL0 = 1.0D0
CRATE = 0.7D0
HOLD = H
NSLP = 0
IPUP = MITER
IRET = 3
C Initialize switching parameters. METH = 1 is assumed initially. -----
ICOUNT = 20
IRFLAG = 0
PDEST = 0.0D0
PDLAST = 0.0D0
RATIO = 5.0D0
CALL DCFODE (2, ELCO, TESCO)
DO 10 I = 1,5
10 CM2(I) = TESCO(2,I)*ELCO(I+1,I)
CALL DCFODE (1, ELCO, TESCO)
DO 20 I = 1,12
20 CM1(I) = TESCO(2,I)*ELCO(I+1,I)
GO TO 150
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, DCFODE is called to reset
C the coefficients of the method.
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. MUSED) GO TO 160
CALL DCFODE (METH, ELCO, TESCO)
IALTH = L
IRET = 1
C-----------------------------------------------------------------------
C The el vector and related constants are reset
C whenever the order NQ is changed, or at the start of the problem.
C-----------------------------------------------------------------------
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/(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 = MAX(RH,HMIN/ABS(H))
175 RH = MIN(RH,RMAX)
RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH)
C-----------------------------------------------------------------------
C If METH = 1, also restrict the new step size by the stability region.
C If this reduces H, set IRFLAG to 1 so that if there are roundoff
C problems later, we can assume that is the cause of the trouble.
C-----------------------------------------------------------------------
IF (METH .EQ. 2) GO TO 178
IRFLAG = 0
PDH = MAX(ABS(H)*PDLAST,0.000001D0)
IF (RH*PDH*1.00001D0 .LT. SM1(NQ)) GO TO 178
RH = SM1(NQ)/PDH
IRFLAG = 1
178 CONTINUE
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 (ABS(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
PNORM = DMNORM (N, YH1, EWT)
C-----------------------------------------------------------------------
C Up to MAXCOR corrector iterations are taken. A convergence test is
C made on the RMS-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
RATE = 0.0D0
DEL = 0.0D0
DO 230 I = 1,N
230 Y(I) = YH(I,1)
CALL F (NEQ, TN, Y, SAVF)
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-----------------------------------------------------------------------
CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC)
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 = DMNORM (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 = DMNORM (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
C We first check for a change of iterates that is the size of
C roundoff error. If this occurs, the iteration has converged, and a
C new rate estimate is not formed.
C In all other cases, force at least two iterations to estimate a
C local Lipschitz constant estimate for Adams methods.
C On convergence, form PDEST = local maximum Lipschitz constant
C estimate. PDLAST is the most recent nonzero estimate.
C-----------------------------------------------------------------------
400 CONTINUE
IF (DEL .LE. 100.0D0*PNORM*UROUND) GO TO 450
IF (M .EQ. 0 .AND. METH .EQ. 1) GO TO 405
IF (M .EQ. 0) GO TO 402
RM = 1024.0D0
IF (DEL .LE. 1024.0D0*DELP) RM = DEL/DELP
RATE = MAX(RATE,RM)
CRATE = MAX(0.2D0*CRATE,RM)
402 DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT)
IF (DCON .GT. 1.0D0) GO TO 405
PDEST = MAX(PDEST,RATE/ABS(H*EL(1)))
IF (PDEST .NE. 0.0D0) PDLAST = PDEST
GO TO 450
405 CONTINUE
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
CALL F (NEQ, TN, Y, SAVF)
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 (ABS(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 = DMNORM (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 Decrease ICOUNT by 1, and if it is -1, consider switching methods.
C If a method switch is made, reset various parameters,
C rescale the YH array, and exit. If there is no switch,
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
MUSED = METH
DO 460 J = 1,L
DO 460 I = 1,N
460 YH(I,J) = YH(I,J) + EL(J)*ACOR(I)
ICOUNT = ICOUNT - 1
IF (ICOUNT .GE. 0) GO TO 488
IF (METH .EQ. 2) GO TO 480
C-----------------------------------------------------------------------
C We are currently using an Adams method. Consider switching to BDF.
C If the current order is greater than 5, assume the problem is
C not stiff, and skip this section.
C If the Lipschitz constant and error estimate are not polluted
C by roundoff, go to 470 and perform the usual test.
C Otherwise, switch to the BDF methods if the last step was
C restricted to insure stability (irflag = 1), and stay with Adams
C method if not. When switching to BDF with polluted error estimates,
C in the absence of other information, double the step size.
C
C When the estimates are OK, we make the usual test by computing
C the step size we could have (ideally) used on this step,
C with the current (Adams) method, and also that for the BDF.
C If NQ .gt. MXORDS, we consider changing to order MXORDS on switching.
C Compare the two step sizes to decide whether to switch.
C The step size advantage must be at least RATIO = 5 to switch.
C-----------------------------------------------------------------------
IF (NQ .GT. 5) GO TO 488
IF (DSM .GT. 100.0D0*PNORM*UROUND .AND. PDEST .NE. 0.0D0)
1 GO TO 470
IF (IRFLAG .EQ. 0) GO TO 488
RH2 = 2.0D0
NQM2 = MIN(NQ,MXORDS)
GO TO 478
470 CONTINUE
EXSM = 1.0D0/L
RH1 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0)
RH1IT = 2.0D0*RH1
PDH = PDLAST*ABS(H)
IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQ)/PDH
RH1 = MIN(RH1,RH1IT)
IF (NQ .LE. MXORDS) GO TO 474
NQM2 = MXORDS
LM2 = MXORDS + 1
EXM2 = 1.0D0/LM2
LM2P1 = LM2 + 1
DM2 = DMNORM (N, YH(1,LM2P1), EWT)/CM2(MXORDS)
RH2 = 1.0D0/(1.2D0*DM2**EXM2 + 0.0000012D0)
GO TO 476
474 DM2 = DSM*(CM1(NQ)/CM2(NQ))
RH2 = 1.0D0/(1.2D0*DM2**EXSM + 0.0000012D0)
NQM2 = NQ
476 CONTINUE
IF (RH2 .LT. RATIO*RH1) GO TO 488
C THE SWITCH TEST PASSED. RESET RELEVANT QUANTITIES FOR BDF. ----------
478 RH = RH2
ICOUNT = 20
METH = 2
MITER = JTYP
PDLAST = 0.0D0
NQ = NQM2
L = NQ + 1
GO TO 170
C-----------------------------------------------------------------------
C We are currently using a BDF method. Consider switching to Adams.
C Compute the step size we could have (ideally) used on this step,
C with the current (BDF) method, and also that for the Adams.
C If NQ .gt. MXORDN, we consider changing to order MXORDN on switching.
C Compare the two step sizes to decide whether to switch.
C The step size advantage must be at least 5/RATIO = 1 to switch.
C If the step size for Adams would be so small as to cause
C roundoff pollution, we stay with BDF.
C-----------------------------------------------------------------------
480 CONTINUE
EXSM = 1.0D0/L
IF (MXORDN .GE. NQ) GO TO 484
NQM1 = MXORDN
LM1 = MXORDN + 1
EXM1 = 1.0D0/LM1
LM1P1 = LM1 + 1
DM1 = DMNORM (N, YH(1,LM1P1), EWT)/CM1(MXORDN)
RH1 = 1.0D0/(1.2D0*DM1**EXM1 + 0.0000012D0)
GO TO 486
484 DM1 = DSM*(CM2(NQ)/CM1(NQ))
RH1 = 1.0D0/(1.2D0*DM1**EXSM + 0.0000012D0)
NQM1 = NQ
EXM1 = EXSM
486 RH1IT = 2.0D0*RH1
PDH = PDNORM*ABS(H)
IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQM1)/PDH
RH1 = MIN(RH1,RH1IT)
RH2 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0)
IF (RH1*RATIO .LT. 5.0D0*RH2) GO TO 488
ALPHA = MAX(0.001D0,RH1)
DM1 = (ALPHA**EXM1)*DM1
IF (DM1 .LE. 1000.0D0*UROUND*PNORM) GO TO 488
C The switch test passed. Reset relevant quantities for Adams. --------
RH = RH1
ICOUNT = 20
METH = 1
MITER = 0
PDLAST = 0.0D0
NQ = NQM1
L = NQ + 1
GO TO 170
C
C No method switch is being made. Do the usual step/order selection. --
488 CONTINUE
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 (ABS(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 = DMNORM (N, SAVF, EWT)/TESCO(3,NQ)
EXUP = 1.0D0/(L+1)
RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0)
540 EXSM = 1.0D0/L
RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0)
RHDN = 0.0D0
IF (NQ .EQ. 1) GO TO 550
DDN = DMNORM (N, YH(1,L), EWT)/TESCO(1,NQ)
EXDN = 1.0D0/NQ
RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0)
C If METH = 1, limit RH according to the stability region also. --------
550 IF (METH .EQ. 2) GO TO 560
PDH = MAX(ABS(H)*PDLAST,0.000001D0)
IF (L .LT. LMAX) RHUP = MIN(RHUP,SM1(L)/PDH)
RHSM = MIN(RHSM,SM1(NQ)/PDH)
IF (NQ .GT. 1) RHDN = MIN(RHDN,SM1(NQ-1)/PDH)
PDEST = 0.0D0
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)/L
DO 600 I = 1,N
600 YH(I,NEWQ+1) = ACOR(I)*R
GO TO 630
610 IALTH = 3
GO TO 700
C If METH = 1 and H is restricted by stability, bypass 10 percent test.
620 IF (METH .EQ. 2) GO TO 622
IF (RH*PDH*1.00001D0 .GE. SM1(NEWQ)) GO TO 625
622 IF (KFLAG .EQ. 0 .AND. RH .LT. 1.1D0) GO TO 610
625 IF (KFLAG .LE. -2) RH = MIN(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 = MAX(HMIN/ABS(H),RH)
H = H*RH
DO 645 I = 1,N
645 Y(I) = YH(I,1)
CALL F (NEQ, TN, Y, SAVF)
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 DSTODA ----------------------
END