[2696] | 1 | SUBROUTINE INTEGRATE( TIN, TOUT ) |
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| 2 | |
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| 3 | USE KPP_ROOT_global |
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| 4 | |
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| 5 | ! TIN - Start Time |
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| 6 | KPP_REAL TIN |
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| 7 | ! TOUT - End Time |
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| 8 | KPP_REAL TOUT |
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| 9 | |
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| 10 | INTEGER INFO(5) |
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| 11 | |
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| 12 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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| 13 | |
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| 14 | INFO(1) = Autonomous |
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| 15 | |
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| 16 | call ROS2(NVAR,TIN,TOUT,STEPMIN,STEPMAX, & |
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| 17 | STEPMIN,VAR,ATOL,RTOL, & |
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| 18 | Info,FUNC_CHEM,JAC_CHEM) |
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| 19 | |
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| 20 | |
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| 21 | END SUBROUTINE INTEGRATE |
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| 22 | |
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| 23 | |
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| 24 | |
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| 25 | |
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| 26 | SUBROUTINE ROS2(N,T,Tnext,Hmin,Hmax,Hstart, & |
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| 27 | y,AbsTol,RelTol, & |
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| 28 | Info,FUNC_CHEM,JAC_CHEM) |
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| 29 | |
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| 30 | USE KPP_ROOT_params |
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| 31 | USE KPP_ROOT_Jacobian_sparsity |
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| 32 | IMPLICIT NONE |
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| 33 | |
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| 34 | ! INPUT ARGUMENTS: |
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| 35 | ! y = Vector of (NVAR) concentrations, contains the |
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| 36 | ! initial values on input |
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| 37 | ! [T, Tnext] = the integration interval |
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| 38 | ! Hmin, Hmax = lower and upper bounds for the selected step-size. |
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| 39 | ! Note that for Step = Hmin the current computed |
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| 40 | ! solution is unconditionally accepted by the error |
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| 41 | ! control mechanism. |
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| 42 | ! AbsTol, RelTol = (NVAR) dimensional vectors of |
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| 43 | ! componentwise absolute and relative tolerances. |
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| 44 | ! FUNC_CHEM = name of routine of derivatives. KPP syntax. |
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| 45 | ! See the header below. |
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| 46 | ! JAC_CHEM = name of routine that computes the Jacobian, in |
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| 47 | ! sparse format. KPP syntax. See the header below. |
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| 48 | ! Info(1) = 1 for autonomous system |
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| 49 | ! = 0 for nonautonomous system |
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| 50 | ! Info(2) = 1 for third order embedded formula |
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| 51 | ! = 0 for first order embedded formula |
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| 52 | ! |
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| 53 | ! Note: Stage 3 used to build strongly A-stable order 3 formula for error control |
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| 54 | ! Embed3 = (Info(2).EQ.1) |
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| 55 | ! if Embed3 = .true. then the third order embedded formula is used |
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| 56 | ! .false. then a first order embedded formula is used |
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| 57 | ! |
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| 58 | ! |
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| 59 | ! OUTPUT ARGUMENTS: |
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| 60 | ! y = the values of concentrations at Tend. |
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| 61 | ! T = equals Tend on output. |
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| 62 | ! Info(2) = # of FUNC_CHEM calls. |
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| 63 | ! Info(3) = # of JAC_CHEM calls. |
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| 64 | ! Info(4) = # of accepted steps. |
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| 65 | ! Info(5) = # of rejected steps. |
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| 66 | |
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| 67 | KPP_REAL K1(NVAR), K2(NVAR), K3(NVAR) |
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| 68 | KPP_REAL F1(NVAR), JAC(LU_NONZERO) |
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| 69 | KPP_REAL DFDT(NVAR) |
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| 70 | KPP_REAL Hmin,Hmax,Hnew,Hstart,ghinv,uround |
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| 71 | KPP_REAL y(NVAR), ynew(NVAR) |
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| 72 | KPP_REAL AbsTol(NVAR), RelTol(NVAR) |
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| 73 | KPP_REAL T, Tnext, H, Hold, Tplus |
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| 74 | KPP_REAL ERR, factor, facmax |
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| 75 | KPP_REAL tau, beta, elo, dround, a21, c31, c32 |
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| 76 | KPP_REAL gamma3, d1, d2, d3, gam |
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| 77 | INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier |
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| 78 | INTEGER Info(5) |
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| 79 | LOGICAL IsReject, Autonomous, Embed3 |
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| 80 | EXTERNAL FUNC_CHEM, JAC_CHEM |
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| 81 | |
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| 82 | KPP_REAL gamma, m1, m2, alpha, beta1, beta2, delta, w, e |
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| 83 | |
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| 84 | ! Initialization of counters, etc. |
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| 85 | Autonomous = Info(1) .EQ. 1 |
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| 86 | Embed3 = Info(2) .EQ. 1 |
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| 87 | uround = 1.d-15 |
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| 88 | dround = dsqrt(uround) |
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| 89 | H = DMAX1(1.d-8, Hmin) |
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| 90 | Tplus = T |
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| 91 | IsReject = .false. |
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| 92 | Naccept = 0 |
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| 93 | Nreject = 0 |
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| 94 | Nfcn = 0 |
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| 95 | Njac = 0 |
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| 96 | |
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| 97 | ! Method Parameters |
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| 98 | gamma = 1.d0 + 1.d0/sqrt(2.d0) |
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| 99 | a21 = - 1.d0/gamma |
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| 100 | m1 = -3.d0/(2.d0*gamma) |
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| 101 | m2 = -1.d0/(2.d0*gamma) |
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| 102 | c31 = -1.0D0/gamma**2*(1.0D0-7.0D0*gamma+9.0D0*gamma**2) & |
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| 103 | /(-1.0D0+2.0D0*gamma) |
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| 104 | c32 = -1.0D0/gamma**2*(1.0D0-6.0D0*gamma+6.0D0*gamma**2) & |
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| 105 | /(-1.0D0+2.0D0*gamma)/2 |
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| 106 | gamma3 = 0.5D0 - 2*gamma |
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| 107 | d1 = ((-9.0D0*gamma+8.0D0*gamma**2+2.0D0)/gamma**2/ & |
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| 108 | (-1.0D0+2*gamma))/6.0D0 |
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| 109 | d2 = ((-1.0D0+3.0D0*gamma)/gamma**2/(-1.0D0+2.0D0*gamma))/6.0D0 |
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| 110 | d3 = -1.0D0/(3.0D0*gamma) |
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| 111 | |
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| 112 | ! === Starting the time loop === |
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| 113 | 10 CONTINUE |
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| 114 | Tplus = T + H |
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| 115 | if ( Tplus .gt. Tnext ) then |
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| 116 | H = Tnext - T |
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| 117 | Tplus = Tnext |
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| 118 | end if |
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| 119 | |
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| 120 | call JAC_CHEM(NVAR, T, y, JAC) |
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| 121 | |
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| 122 | Njac = Njac+1 |
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| 123 | ghinv = -1.0d0/(gamma*H) |
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| 124 | DO j=1,NVAR |
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| 125 | JAC(LU_DIAG(j)) = JAC(LU_DIAG(j)) + ghinv |
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| 126 | END DO |
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| 127 | CALL KppDecomp (JAC, ier) |
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| 128 | |
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| 129 | if (ier.ne.0) then |
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| 130 | if ( H.gt.Hmin) then |
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| 131 | H = 5.0d-1*H |
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| 132 | go to 10 |
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| 133 | else |
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| 134 | print *,'IER <> 0, H=',H |
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| 135 | stop |
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| 136 | end if |
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| 137 | end if |
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| 138 | |
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| 139 | call FUNC_CHEM(NVAR, T, y, F1) |
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| 140 | |
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| 141 | ! ====== NONAUTONOMOUS CASE =============== |
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| 142 | IF (.not. Autonomous) THEN |
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| 143 | tau = dsign(dround*dmax1( 1.0d-6, dabs(T) ), T) |
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| 144 | call FUNC_CHEM(NVAR, T+tau, y, K2) |
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| 145 | nfcn=nfcn+1 |
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| 146 | DO j = 1,NVAR |
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| 147 | DFDT(j) = ( K2(j)-F1(j) )/tau |
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| 148 | END DO |
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| 149 | END IF ! .NOT.Autonomous |
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| 150 | |
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| 151 | ! ----- STAGE 1 ----- |
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| 152 | DO j = 1,NVAR |
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| 153 | K1(j) = F1(j) |
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| 154 | END DO |
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| 155 | IF (.NOT.Autonomous) THEN |
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| 156 | delta = gamma*H |
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| 157 | DO j = 1,NVAR |
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| 158 | K1(j) = K1(j) + delta*DFDT(j) |
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| 159 | END DO |
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| 160 | END IF ! .NOT.Autonomous |
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| 161 | call KppSolve (JAC, K1) |
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| 162 | |
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| 163 | ! ----- STAGE 2 ----- |
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| 164 | DO j = 1,NVAR |
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| 165 | ynew(j) = y(j) + a21*K1(j) |
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| 166 | END DO |
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| 167 | call FUNC_CHEM(NVAR, T+H, ynew, F1) |
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| 168 | nfcn=nfcn+1 |
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| 169 | beta = 2.d0/(gamma*H) |
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| 170 | DO j = 1,NVAR |
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| 171 | K2(j) = F1(j) + beta*K1(j) |
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| 172 | END DO |
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| 173 | IF (.NOT. Autonomous) THEN |
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| 174 | delta = -gamma*H |
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| 175 | DO j = 1,NVAR |
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| 176 | K2(j) = K2(j) + delta*DFDT(j) |
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| 177 | END DO |
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| 178 | END IF ! .NOT.Autonomous |
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| 179 | call KppSolve (JAC, K2) |
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| 180 | |
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| 181 | ! ----- STAGE 3 ----- |
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| 182 | IF (Embed3) THEN |
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| 183 | beta1 = -c31/H |
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| 184 | beta2 = -c32/H |
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| 185 | delta = gamma3*H |
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| 186 | DO j = 1,NVAR |
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| 187 | K3(j) = F1(j) + beta1*K1(j) + beta2*K2(j) |
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| 188 | END DO |
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| 189 | IF (.NOT.Autonomous) THEN |
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| 190 | DO j = 1,NVAR |
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| 191 | K3(j) = K3(j) + delta*DFDT(j) |
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| 192 | END DO |
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| 193 | END IF ! .NOT.Autonomous |
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| 194 | CALL KppSolve (JAC, K3) |
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| 195 | END IF ! Embed3 |
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| 196 | |
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| 197 | |
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| 198 | |
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| 199 | ! ---- The Solution --- |
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| 200 | DO j = 1,NVAR |
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| 201 | ynew(j) = y(j) + m1*K1(j) + m2*K2(j) |
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| 202 | END DO |
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| 203 | |
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| 204 | |
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| 205 | ! ====== Error estimation ======== |
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| 206 | |
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| 207 | ERR=0.d0 |
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| 208 | DO i=1,NVAR |
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| 209 | w = AbsTol(i) + RelTol(i)*DMAX1(DABS(y(i)),DABS(ynew(i))) |
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| 210 | IF ( Embed3 ) THEN |
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| 211 | e = d1*K1(i) + d2*K2(i) + d3*K3(i) |
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| 212 | ELSE |
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| 213 | e = 1.d0/(2.d0*gamma)*(K1(i)+K2(i)) |
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| 214 | END IF ! Embed3 |
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| 215 | ERR = ERR + ( e/w )**2 |
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| 216 | END DO |
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| 217 | ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) |
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| 218 | |
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| 219 | ! ======= Choose the stepsize =============================== |
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| 220 | |
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| 221 | IF ( Embed3 ) THEN |
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| 222 | elo = 3.0D0 ! estimator local order |
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| 223 | ELSE |
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| 224 | elo = 2.0D0 |
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| 225 | END IF |
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| 226 | factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) |
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| 227 | Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) |
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| 228 | |
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| 229 | ! ======= Rejected/Accepted Step ============================ |
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| 230 | |
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| 231 | IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN |
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| 232 | IsReject = .true. |
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| 233 | H = DMIN1(H/10,Hnew) |
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| 234 | Nreject = Nreject+1 |
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| 235 | ELSE |
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| 236 | DO i=1,NVAR |
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| 237 | y(i) = ynew(i) |
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| 238 | END DO |
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| 239 | T = Tplus |
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| 240 | IF (.NOT. IsReject) THEN |
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| 241 | H = Hnew ! Do not increase stepsize if previous step was rejected |
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| 242 | END IF |
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| 243 | IsReject = .false. |
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| 244 | Naccept = Naccept+1 |
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| 245 | END IF |
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| 246 | |
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| 247 | |
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| 248 | ! ======= End of the time loop =============================== |
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| 249 | IF ( T .lt. Tnext ) GO TO 10 |
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| 250 | |
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| 251 | |
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| 252 | |
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| 253 | ! ======= Output Information ================================= |
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| 254 | Info(2) = Nfcn |
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| 255 | Info(3) = Njac |
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| 256 | Info(4) = Naccept |
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| 257 | Info(5) = Nreject |
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| 258 | |
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| 259 | END SUBROUTINE Ros2 |
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| 260 | |
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| 261 | |
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| 262 | |
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| 263 | SUBROUTINE FUNC_CHEM(N, T, Y, P) |
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| 264 | USE KPP_ROOT_global |
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| 265 | INTEGER N |
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| 266 | KPP_REAL T, Told |
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| 267 | KPP_REAL Y(NVAR), P(NVAR) |
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| 268 | Told = TIME |
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| 269 | TIME = T |
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| 270 | CALL Update_SUN() |
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| 271 | CALL Update_RCONST() |
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| 272 | CALL Fun( Y, FIX, RCONST, P ) |
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| 273 | TIME = Told |
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| 274 | END SUBROUTINE FUNC_CHEM |
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| 275 | |
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| 276 | |
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| 277 | SUBROUTINE JAC_CHEM(N, T, Y, J) |
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| 278 | USE KPP_ROOT_global |
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| 279 | INTEGER N |
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| 280 | KPP_REAL Told, T |
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| 281 | KPP_REAL Y(NVAR), J(LU_NONZERO) |
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| 282 | Told = TIME |
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| 283 | TIME = T |
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| 284 | CALL Update_SUN() |
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| 285 | CALL Update_RCONST() |
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| 286 | CALL Jac_SP( Y, FIX, RCONST, J ) |
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| 287 | TIME = Told |
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| 288 | END SUBROUTINE JAC_CHEM |
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| 289 | |
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| 290 | |
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| 291 | |
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| 292 | |
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| 293 | |
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| 294 | |
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