!----------------------------------------------------------------------------------------------------------------------------------! !()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()! !----------------------------------------------------------------------------------------------------------------------------------! !> !! DSTODA performs one step of the integration of an initial value !! problem for a system of ordinary differential equations. !! !! Note: DSTODA is independent of the value of the iteration method !! indicator MITER, when this is .ne. 0, and hence is independent !! of the type of chord method used, or the Jacobian structure. !! !! Communication with DSTODA is done with the following variables: !! !! Y !! !! : an array of length .ge. N used as the Y argument in !! all calls to F and JAC. !! !! NEQ !! !! : integer array containing problem size in NEQ(1), and !! passed as the NEQ argument in all calls to F and JAC. !! !! YH !! !! : an NYH by LMAX array containing the dependent variables !! and their approximate scaled derivatives, where !! LMAX = MAXORD + 1. YH(i,j+1) contains the approximate !! j-th derivative of y(i), scaled by H**j/factorial(j) !! (j = 0,1,...,NQ). On entry for the first step, the first !! two columns of YH must be set from the initial values. !! !! NYH !! !! : a constant integer .ge. N, the first dimension of YH. !! !! YH1 !! !! : a one-dimensional array occupying the same space as YH. !! !! EWT !! !! : an array of length N containing multiplicative weights !! for local error measurements. Local errors in y(i) are !! compared to 1.0/EWT(i) in various error tests. !! !! SAVF !! !! : an array of working storage, of length N. !! !! ACOR !! !! : a work array of length N, used for the accumulated !! corrections. On a successful return, ACOR(i) contains !! the estimated one-step local error in y(i). !! !! WM,IWM !! !! : real and integer work arrays associated with matrix !! operations in chord iteration (MITER .ne. 0). !! !! PJAC !! !! : name of routine to evaluate and preprocess Jacobian matrix !! and P = I - H*EL0*Jac, if a chord method is being used. !! It also returns an estimate of norm(Jac) in PDNORM. !! !! SLVS !! !! : name of routine to solve linear system in chord iteration. !! !! CCMAX !! !! : maximum relative change in H*EL0 before PJAC is called. !! !! H !! !! : the step size to be attempted on the next step. !! H is altered by the error control algorithm during the !! problem. H can be either positive or negative, but its !! sign must remain constant throughout the problem. !! !! HMIN !! !! : the minimum absolute value of the step size H to be used. !! !! HMXI !! !! : inverse of the maximum absolute value of H to be used. !! HMXI = 0.0 is allowed and corresponds to an infinite HMAX. !! HMIN and HMXI may be changed at any time, but will not !! take effect until the next change of H is considered. !! !! TN !! !! : the independent variable. TN is updated on each step taken. !! !! JSTART !! !! : an integer used for input only, with the following !! values and meanings: !! 0 perform the first step. !! .gt.0 take a new step continuing from the last. !! -1 take the next step with a new value of H, !! N, METH, MITER, and/or matrix parameters. !! -2 take the next step with a new value of H, !! but with other inputs unchanged. !! On return, JSTART is set to 1 to facilitate continuation. !! !! KFLAG !! !! : a completion code with the following meanings: !! 0 the step was succesful. !! -1 the requested error could not be achieved. !! -2 corrector convergence could not be achieved. !! -3 fatal error in PJAC or SLVS. !! A return with KFLAG = -1 or -2 means either !! ABS(H) = HMIN or 10 consecutive failures occurred. !! On a return with KFLAG negative, the values of TN and !! the YH array are as of the beginning of the last !! step, and H is the last step size attempted. !! !! MAXORD !! !! : the maximum order of integration method to be allowed. !! !! MAXCOR !! !! : the maximum number of corrector iterations allowed. !! !! MSBP !! !! : maximum number of steps between PJAC calls (MITER .gt. 0). !! !! MXNCF !! !! : maximum number of convergence failures allowed. !! !! METH !! !! : current method. !! METH = 1 means Adams method (nonstiff) !! METH = 2 means BDF method (stiff) !! METH may be reset by DSTODA. !! !! MITER !! !! : corrector iteration method. !! MITER = 0 means functional iteration. !! MITER = JT .gt. 0 means a chord iteration corresponding !! to Jacobian type JT. (The DLSODA/DLSODAR argument JT is !! communicated here as JTYP, but is not used in DSTODA !! except to load MITER following a method switch.) !! MITER may be reset by DSTODA. !! !! N !! !! : the number of first-order differential equations. !----------------------------------------------------------------------- subroutine dstoda(Neq,Y,Yh,Nyh,Yh1,Ewt,Savf,Acor,Wm,Iwm,f,jac,pjac,slvs) ! integer :: Neq(*) real(kind=dp),intent(inout) :: Y(*) integer :: Nyh real(kind=dp),intent(inout) :: Yh(Nyh,*) real(kind=dp),intent(inout) :: Yh1(*) real(kind=dp) :: Ewt(*) real(kind=dp),intent(inout) :: Savf(*) real(kind=dp),intent(inout) :: Acor(*) real(kind=dp) :: Wm(*) integer :: Iwm(*) external f external jac external pjac external slvs real(kind=dp) :: alpha, dcon, ddn, del, delp, dm1, dm2, dsm, dup, exdn, exm1, exm2, exsm, exup, pdh, pnorm, r, & & rate, rh, rh1, rh1it, rh2, rhdn, rhsm, rhup, rm, told integer :: i, i1, iredo, iret, j, jb, lm1, lm1p1, lm2, lm2p1, m, ncf, newq, nqm1, nqm2 real(kind=dp),parameter :: sm1(12)=& & [0.5D0, 0.575D0, 0.55D0, 0.45D0, 0.35D0, 0.25D0, 0.20D0, 0.15D0, 0.10D0, 0.075D0, 0.050D0, 0.025D0] dls1%kflag = 0 told = dls1%tn ncf = 0 dls1%ierpj = 0 dls1%iersl = 0 dls1%jcur = 0 dls1%icf = 0 delp = 0.0D0 if ( dls1%jstart>0 ) goto 400 if ( dls1%jstart==-1 ) then !----------------------------------------------------------------------- ! The following block handles preliminaries needed when JSTART = -1. ! IPUP is set to MITER to force a matrix update. ! If an order increase is about to be considered (IALTH = 1), ! IALTH is reset to 2 to postpone consideration one more step. ! If the caller has changed METH, DCFODE is called to reset ! the coefficients of the method. ! If H is to be changed, YH must be rescaled. ! If H or METH is being changed, IALTH is reset to L = NQ + 1 ! to prevent further changes in H for that many steps. !----------------------------------------------------------------------- dls1%ipup = dls1%miter dls1%lmax = dls1%maxord + 1 if ( dls1%ialth==1 ) dls1%ialth = 2 if ( dls1%meth==dlsa%mused ) goto 200 call dcfode(dls1%meth,dls1%elco,dls1%tesco) dls1%ialth = dls1%l iret = 1 else if ( dls1%jstart==-2 ) goto 200 !----------------------------------------------------------------------- ! On the first call, the order is set to 1, and other variables are ! initialized. RMAX is the maximum ratio by which H can be increased ! in a single step. It is initially 1.E4 to compensate for the small ! initial H, but then is normally equal to 10. If a failure ! occurs (in corrector convergence or error test), RMAX is set at 2 ! for the next increase. ! DCFODE is called to get the needed coefficients for both methods. !----------------------------------------------------------------------- dls1%lmax = dls1%maxord + 1 dls1%nq = 1 dls1%l = 2 dls1%ialth = 2 dls1%rmax = 10000.0D0 dls1%rc = 0.0D0 dls1%el0 = 1.0D0 dls1%crate = 0.7D0 dls1%hold = dls1%h dls1%nslp = 0 dls1%ipup = dls1%miter iret = 3 ! Initialize switching parameters. METH = 1 is assumed initially. ----- dlsa%icount = 20 dlsa%irflag = 0 dlsa%pdest = 0.0D0 dlsa%pdlast = 0.0D0 dlsa%ratio = 5.0D0 call dcfode(2,dls1%elco,dls1%tesco) do i = 1, 5 dlsa%cm2(i) = dls1%tesco(2,i)*dls1%elco(i+1,i) enddo call dcfode(1,dls1%elco,dls1%tesco) do i = 1, 12 dlsa%cm1(i) = dls1%tesco(2,i)*dls1%elco(i+1,i) enddo endif !----------------------------------------------------------------------- ! The dls1%el vector and related constants are reset ! whenever the order NQ is changed, or at the start of the problem. !----------------------------------------------------------------------- 100 continue do i = 1, dls1%l dls1%el(i) = dls1%elco(i,dls1%nq) enddo dls1%nqnyh = dls1%nq*Nyh dls1%rc = dls1%rc*dls1%el(1)/dls1%el0 dls1%el0 = dls1%el(1) dls1%conit = 0.5D0/(dls1%nq+2) select case (iret) case (2) rh = max(rh,dls1%hmin/abs(dls1%h)) goto 300 case (3) goto 400 case default endselect !----------------------------------------------------------------------- ! If H is being changed, the H ratio RH is checked against ! RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to ! L = NQ + 1 to prevent a change of H for that many steps, unless ! forced by a convergence or error test failure. !----------------------------------------------------------------------- 200 continue if ( dls1%h==dls1%hold ) goto 400 rh = dls1%h/dls1%hold dls1%h = dls1%hold iredo = 3 300 continue rh = min(rh,dls1%rmax) rh = rh/max(1.0D0,abs(dls1%h)*dls1%hmxi*rh) !----------------------------------------------------------------------- ! If METH = 1, also restrict the new step size by the stability region. ! If this reduces H, set IRFLAG to 1 so that if there are roundoff ! problems later, we can assume that is the cause of the trouble. !----------------------------------------------------------------------- if ( dls1%meth/=2 ) then dlsa%irflag = 0 pdh = max(abs(dls1%h)*dlsa%pdlast,0.000001D0) if ( rh*pdh*1.00001D0>=sm1(dls1%nq) ) then rh = sm1(dls1%nq)/pdh dlsa%irflag = 1 endif endif r = 1.0D0 do j = 2, dls1%l r = r*rh do i = 1, dls1%n Yh(i,j) = Yh(i,j)*r enddo enddo dls1%h = dls1%h*rh dls1%rc = dls1%rc*rh dls1%ialth = dls1%l if ( iredo==0 ) then dls1%rmax = 10.0D0 goto 1300 endif !----------------------------------------------------------------------- ! This section computes the predicted values by effectively ! multiplying the YH array by the Pascal triangle matrix. ! RC is the ratio of new to old values of the coefficient H*EL(1). ! When RC differs from 1 by more than CCMAX, IPUP is set to MITER ! to force PJAC to be called, if a Jacobian is involved. ! In any case, PJAC is called at least every MSBP steps. !----------------------------------------------------------------------- 400 continue if ( abs(dls1%rc-1.0D0)>dls1%ccmax ) dls1%ipup = dls1%miter if ( dls1%nst>=dls1%nslp+dls1%msbp ) dls1%ipup = dls1%miter dls1%tn = dls1%tn + dls1%h i1 = dls1%nqnyh + 1 do jb = 1, dls1%nq i1 = i1 - Nyh ! DIR$ IVDEP do i = i1, dls1%nqnyh Yh1(i) = Yh1(i) + Yh1(i+Nyh) enddo enddo pnorm = dmnorm(dls1%n,Yh1,Ewt) !----------------------------------------------------------------------- ! Up to MAXCOR corrector iterations are taken. A convergence test is ! made on the RMS-norm of each correction, weighted by the error ! weight vector EWT. The sum of the corrections is accumulated in the ! vector ACOR(i). The YH array is not altered in the corrector loop. !----------------------------------------------------------------------- 500 continue m = 0 rate = 0.0D0 del = 0.0D0 do i = 1, dls1%n Y(i) = Yh(i,1) enddo call f(Neq,dls1%tn,Y,Savf) dls1%nfe = dls1%nfe + 1 if ( dls1%ipup>0 ) then !----------------------------------------------------------------------- ! If indicated, the matrix P = I - H*EL(1)*J is reevaluated and ! preprocessed before starting the corrector iteration. IPUP is set ! to 0 as an indicator that this has been done. !----------------------------------------------------------------------- call pjac(Neq,Y,Yh,Nyh,Ewt,Acor,Savf,Wm,Iwm,f,jac) dls1%ipup = 0 dls1%rc = 1.0D0 dls1%nslp = dls1%nst dls1%crate = 0.7D0 if ( dls1%ierpj/=0 ) goto 800 endif do i = 1, dls1%n Acor(i) = 0.0D0 enddo 600 continue if ( dls1%miter/=0 ) then !----------------------------------------------------------------------- ! In the case of the chord method, compute the corrector error, ! and solve the linear system with that as right-hand side and ! P as coefficient matrix. !----------------------------------------------------------------------- do i = 1, dls1%n Y(i) = dls1%h*Savf(i) - (Yh(i,2)+Acor(i)) enddo call slvs(Wm,Iwm,Y,Savf) if ( dls1%iersl<0 ) goto 800 if ( dls1%iersl>0 ) goto 700 del = dmnorm(dls1%n,Y,Ewt) do i = 1, dls1%n Acor(i) = Acor(i) + Y(i) Y(i) = Yh(i,1) + dls1%el(1)*Acor(i) enddo else !----------------------------------------------------------------------- ! In the case of functional iteration, update Y directly from ! the result of the last function evaluation. !----------------------------------------------------------------------- do i = 1, dls1%n Savf(i) = dls1%h*Savf(i) - Yh(i,2) Y(i) = Savf(i) - Acor(i) enddo del = dmnorm(dls1%n,Y,Ewt) do i = 1, dls1%n Y(i) = Yh(i,1) + dls1%el(1)*Savf(i) Acor(i) = Savf(i) enddo endif !----------------------------------------------------------------------- ! Test for convergence. If M .gt. 0, an estimate of the convergence ! rate constant is stored in CRATE, and this is used in the test. ! ! We first check for a change of iterates that is the size of ! roundoff error. If this occurs, the iteration has converged, and a ! new rate estimate is not formed. ! In all other cases, force at least two iterations to estimate a ! local Lipschitz constant estimate for Adams methods. ! On convergence, form PDEST = local maximum Lipschitz constant ! estimate. PDLAST is the most recent nonzero estimate. !----------------------------------------------------------------------- if ( del<=100.0D0*pnorm*dls1%uround ) goto 900 if ( m/=0 .or. dls1%meth/=1 ) then if ( m/=0 ) then rm = 1024.0D0 if ( del<=1024.0D0*delp ) rm = del/delp rate = max(rate,rm) dls1%crate = max(0.2D0*dls1%crate,rm) endif dcon = del*min(1.0D0,1.5D0*dls1%crate)/(dls1%tesco(2,dls1%nq)*dls1%conit) if ( dcon<=1.0D0 ) then dlsa%pdest = max(dlsa%pdest,rate/abs(dls1%h*dls1%el(1))) if ( dlsa%pdest/=0.0D0 ) dlsa%pdlast = dlsa%pdest goto 900 endif endif m = m + 1 if ( m/=dls1%maxcor ) then if ( m<2 .or. del<=2.0D0*delp ) then delp = del call f(Neq,dls1%tn,Y,Savf) dls1%nfe = dls1%nfe + 1 goto 600 endif endif !----------------------------------------------------------------------- ! The corrector iteration failed to converge. ! If MITER .ne. 0 and the Jacobian is out of date, PJAC is called for ! the next try. Otherwise the YH array is retracted to its values ! before prediction, and H is reduced, if possible. If H cannot be ! reduced or MXNCF failures have occurred, exit with KFLAG = -2. !----------------------------------------------------------------------- 700 continue if ( dls1%miter/=0 .and. dls1%jcur/=1 ) then dls1%icf = 1 dls1%ipup = dls1%miter goto 500 endif 800 continue dls1%icf = 2 ncf = ncf + 1 dls1%rmax = 2.0D0 dls1%tn = told i1 = dls1%nqnyh + 1 do jb = 1, dls1%nq i1 = i1 - Nyh ! DIR$ IVDEP do i = i1, dls1%nqnyh Yh1(i) = Yh1(i) - Yh1(i+Nyh) enddo enddo if ( dls1%ierpj<0 .or. dls1%iersl<0 ) then dls1%kflag = -3 goto 1400 elseif ( abs(dls1%h)<=dls1%hmin*1.00001D0 ) then dls1%kflag = -2 goto 1400 elseif ( ncf==dls1%mxncf ) then dls1%kflag = -2 goto 1400 else rh = 0.25D0 dls1%ipup = dls1%miter iredo = 1 rh = max(rh,dls1%hmin/abs(dls1%h)) goto 300 endif !----------------------------------------------------------------------- ! The corrector has converged. JCUR is set to 0 ! to signal that the Jacobian involved may need updating later. ! The local error test is made and control passes to statement 500 ! if it fails. !----------------------------------------------------------------------- 900 continue dls1%jcur = 0 if ( m==0 ) dsm = del/dls1%tesco(2,dls1%nq) if ( m>0 ) dsm = dmnorm(dls1%n,Acor,Ewt)/dls1%tesco(2,dls1%nq) if ( dsm>1.0D0 ) then !----------------------------------------------------------------------- ! The error test failed. KFLAG keeps track of multiple failures. ! Restore TN and the YH array to their previous values, and prepare ! to try the step again. Compute the optimum step size for this or ! one lower order. After 2 or more failures, H is forced to decrease ! by a factor of 0.2 or less. !----------------------------------------------------------------------- dls1%kflag = dls1%kflag - 1 dls1%tn = told i1 = dls1%nqnyh + 1 do jb = 1, dls1%nq i1 = i1 - Nyh ! DIR$ IVDEP do i = i1, dls1%nqnyh Yh1(i) = Yh1(i) - Yh1(i+Nyh) enddo enddo dls1%rmax = 2.0D0 if ( abs(dls1%h)<=dls1%hmin*1.00001D0 ) then !----------------------------------------------------------------------- ! All returns are made through this section. H is saved in HOLD ! to allow the caller to change H on the next step. !----------------------------------------------------------------------- dls1%kflag = -1 goto 1400 elseif ( dls1%kflag<=-3 ) then !----------------------------------------------------------------------- ! Control reaches this section if 3 or more failures have occured. ! If 10 failures have occurred, exit with KFLAG = -1. ! It is assumed that the derivatives that have accumulated in the ! YH array have errors of the wrong order. Hence the first ! derivative is recomputed, and the order is set to 1. Then ! H is reduced by a factor of 10, and the step is retried, ! until it succeeds or H reaches HMIN. !----------------------------------------------------------------------- if ( dls1%kflag==-10 ) then dls1%kflag = -1 goto 1400 else rh = 0.1D0 rh = max(dls1%hmin/abs(dls1%h),rh) dls1%h = dls1%h*rh do i = 1, dls1%n Y(i) = Yh(i,1) enddo call f(Neq,dls1%tn,Y,Savf) dls1%nfe = dls1%nfe + 1 do i = 1, dls1%n Yh(i,2) = dls1%h*Savf(i) enddo dls1%ipup = dls1%miter dls1%ialth = 5 if ( dls1%nq==1 ) goto 400 dls1%nq = 1 dls1%l = 2 iret = 3 goto 100 endif else iredo = 2 rhup = 0.0D0 endif else !----------------------------------------------------------------------- ! After a successful step, update the YH array. ! Decrease ICOUNT by 1, and if it is -1, consider switching methods. ! If a method switch is made, reset various parameters, ! rescale the YH array, and exit. If there is no switch, ! consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. ! If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for ! use in a possible order increase on the next step. ! If a change in H is considered, an increase or decrease in order ! by one is considered also. A change in H is made only if it is by a ! factor of at least 1.1. If not, IALTH is set to 3 to prevent ! testing for that many steps. !----------------------------------------------------------------------- dls1%kflag = 0 iredo = 0 dls1%nst = dls1%nst + 1 dls1%hu = dls1%h dls1%nqu = dls1%nq dlsa%mused = dls1%meth do j = 1, dls1%l do i = 1, dls1%n Yh(i,j) = Yh(i,j) + dls1%el(j)*Acor(i) enddo enddo dlsa%icount = dlsa%icount - 1 if ( dlsa%icount<0 ) then if ( dls1%meth==2 ) then !----------------------------------------------------------------------- ! We are currently using a BDF method. Consider switching to Adams. ! Compute the step size we could have (ideally) used on this step, ! with the current (BDF) method, and also that for the Adams. ! If NQ .gt. MXORDN, we consider changing to order MXORDN on switching. ! Compare the two step sizes to decide whether to switch. ! The step size advantage must be at least 5/RATIO = 1 to switch. ! If the step size for Adams would be so small as to cause ! roundoff pollution, we stay with BDF. !----------------------------------------------------------------------- exsm = 1.0D0/dls1%l if ( dlsa%mxordn>=dls1%nq ) then dm1 = dsm*(dlsa%cm2(dls1%nq)/dlsa%cm1(dls1%nq)) rh1 = 1.0D0/(1.2D0*dm1**exsm+0.0000012D0) nqm1 = dls1%nq exm1 = exsm else nqm1 = dlsa%mxordn lm1 = dlsa%mxordn + 1 exm1 = 1.0D0/lm1 lm1p1 = lm1 + 1 dm1 = dmnorm(dls1%n,Yh(1,lm1p1),Ewt)/dlsa%cm1(dlsa%mxordn) rh1 = 1.0D0/(1.2D0*dm1**exm1+0.0000012D0) endif rh1it = 2.0D0*rh1 pdh = dlsa%pdnorm*abs(dls1%h) if ( pdh*rh1>0.00001D0 ) rh1it = sm1(nqm1)/pdh rh1 = min(rh1,rh1it) rh2 = 1.0D0/(1.2D0*dsm**exsm+0.0000012D0) if ( rh1*dlsa%ratio>=5.0D0*rh2 ) then alpha = max(0.001D0,rh1) dm1 = (alpha**exm1)*dm1 if ( dm1>1000.0D0*dls1%uround*pnorm ) then ! The switch test passed. Reset relevant quantities for Adams. -------- rh = rh1 dlsa%icount = 20 dls1%meth = 1 dls1%miter = 0 dlsa%pdlast = 0.0D0 dls1%nq = nqm1 dls1%l = dls1%nq + 1 rh = max(rh,dls1%hmin/abs(dls1%h)) goto 300 endif endif !----------------------------------------------------------------------- ! We are currently using an Adams method. Consider switching to BDF. ! If the current order is greater than 5, assume the problem is ! not stiff, and skip this section. ! If the Lipschitz constant and error estimate are not polluted ! by roundoff, go to 470 and perform the usual test. ! Otherwise, switch to the BDF methods if the last step was ! restricted to insure stability (dlsa%irflag = 1), and stay with Adams ! method if not. When switching to BDF with polluted error estimates, ! in the absence of other information, double the step size. ! ! When the estimates are OK, we make the usual test by computing ! the step size we could have (ideally) used on this step, ! with the current (Adams) method, and also that for the BDF. ! If NQ .gt. MXORDS, we consider changing to order MXORDS on switching. ! Compare the two step sizes to decide whether to switch. ! The step size advantage must be at least RATIO = 5 to switch. !----------------------------------------------------------------------- elseif ( dls1%nq<=5 ) then if ( dsm>100.0D0*pnorm*dls1%uround .and. dlsa%pdest/=0.0D0 ) then exsm = 1.0D0/dls1%l rh1 = 1.0D0/(1.2D0*dsm**exsm+0.0000012D0) rh1it = 2.0D0*rh1 pdh = dlsa%pdlast*abs(dls1%h) if ( pdh*rh1>0.00001D0 ) rh1it = sm1(dls1%nq)/pdh rh1 = min(rh1,rh1it) if ( dls1%nq<=dlsa%mxords ) then dm2 = dsm*(dlsa%cm1(dls1%nq)/dlsa%cm2(dls1%nq)) rh2 = 1.0D0/(1.2D0*dm2**exsm+0.0000012D0) nqm2 = dls1%nq else nqm2 = dlsa%mxords lm2 = dlsa%mxords + 1 exm2 = 1.0D0/lm2 lm2p1 = lm2 + 1 dm2 = dmnorm(dls1%n,Yh(1,lm2p1),Ewt)/dlsa%cm2(dlsa%mxords) rh2 = 1.0D0/(1.2D0*dm2**exm2+0.0000012D0) endif if ( rh2<dlsa%ratio*rh1 ) goto 950 else if ( dlsa%irflag==0 ) goto 950 rh2 = 2.0D0 nqm2 = min(dls1%nq,dlsa%mxords) endif ! THE SWITCH TEST PASSED. RESET RELEVANT QUANTITIES FOR BDF. ---------- rh = rh2 dlsa%icount = 20 dls1%meth = 2 dls1%miter = dlsa%jtyp dlsa%pdlast = 0.0D0 dls1%nq = nqm2 dls1%l = dls1%nq + 1 rh = max(rh,dls1%hmin/abs(dls1%h)) goto 300 endif endif ! ! No method switch is being made. Do the usual step/order selection. -- 950 continue dls1%ialth = dls1%ialth - 1 if ( dls1%ialth==0 ) then !----------------------------------------------------------------------- ! Regardless of the success or failure of the step, factors ! RHDN, RHSM, and RHUP are computed, by which H could be multiplied ! at order NQ - 1, order NQ, or order NQ + 1, respectively. ! In the case of failure, RHUP = 0.0 to avoid an order increase. ! The largest of these is determined and the new order chosen ! accordingly. If the order is to be increased, we compute one ! additional scaled derivative. !----------------------------------------------------------------------- rhup = 0.0D0 if ( dls1%l/=dls1%lmax ) then do i = 1, dls1%n Savf(i) = Acor(i) - Yh(i,dls1%lmax) enddo dup = dmnorm(dls1%n,Savf,Ewt)/dls1%tesco(3,dls1%nq) exup = 1.0D0/(dls1%l+1) rhup = 1.0D0/(1.4D0*dup**exup+0.0000014D0) endif else if ( dls1%ialth<=1 ) then if ( dls1%l/=dls1%lmax ) then do i = 1, dls1%n Yh(i,dls1%lmax) = Acor(i) enddo endif endif goto 1300 endif endif exsm = 1.0D0/dls1%l rhsm = 1.0D0/(1.2D0*dsm**exsm+0.0000012D0) rhdn = 0.0D0 if ( dls1%nq/=1 ) then ddn = dmnorm(dls1%n,Yh(1,dls1%l),Ewt)/dls1%tesco(1,dls1%nq) exdn = 1.0D0/dls1%nq rhdn = 1.0D0/(1.3D0*ddn**exdn+0.0000013D0) endif ! If METH = 1, limit RH according to the stability region also. -------- if ( dls1%meth/=2 ) then pdh = max(abs(dls1%h)*dlsa%pdlast,0.000001D0) if ( dls1%l<dls1%lmax ) rhup = min(rhup,sm1(dls1%l)/pdh) rhsm = min(rhsm,sm1(dls1%nq)/pdh) if ( dls1%nq>1 ) rhdn = min(rhdn,sm1(dls1%nq-1)/pdh) dlsa%pdest = 0.0D0 endif if ( rhsm>=rhup ) then if ( rhsm>=rhdn ) then newq = dls1%nq rh = rhsm goto 1000 endif elseif ( rhup>rhdn ) then newq = dls1%l rh = rhup if ( rh<1.1D0 ) then dls1%ialth = 3 goto 1300 else r = dls1%el(dls1%l)/dls1%l do i = 1, dls1%n Yh(i,newq+1) = Acor(i)*r enddo goto 1200 endif endif newq = dls1%nq - 1 rh = rhdn if ( dls1%kflag<0 .and. rh>1.0D0 ) rh = 1.0D0 ! If METH = 1 and H is restricted by stability, bypass 10 percent test. 1000 continue if ( dls1%meth/=2 ) then if ( rh*pdh*1.00001D0>=sm1(newq) ) goto 1100 endif if ( dls1%kflag==0 .and. rh<1.1D0 ) then dls1%ialth = 3 goto 1300 endif 1100 continue if ( dls1%kflag<=-2 ) rh = min(rh,0.2D0) !----------------------------------------------------------------------- ! If there is a change of order, reset NQ, L, and the coefficients. ! In any case H is reset according to RH and the YH array is rescaled. ! Then exit from 690 if the step was OK, or redo the step otherwise. !----------------------------------------------------------------------- if ( newq==dls1%nq ) then rh = max(rh,dls1%hmin/abs(dls1%h)) goto 300 endif 1200 continue dls1%nq = newq dls1%l = dls1%nq + 1 iret = 2 goto 100 1300 continue r = 1.0D0/dls1%tesco(2,dls1%nqu) do i = 1, dls1%n Acor(i) = Acor(i)*r enddo 1400 continue dls1%hold = dls1%h dls1%jstart = 1 end subroutine dstoda