[2696] | 1 | |
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| 2 | #define MAX(a,b) ((a) >= (b) ) ?(a):(b) |
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| 3 | #define MIN(b,c) ((b) < (c) ) ?(b):(c) |
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| 4 | #define abs(x) ((x) >= 0 ) ?(x):(-x) |
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| 5 | #define dabs(y) (double)abs(y) |
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| 6 | #define DSQRT(d) (double)pow(d,0.5) |
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| 7 | |
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| 8 | void (*forfun)(int,KPP_REAL,KPP_REAL [],KPP_REAL []); |
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| 9 | void (*forjac)(int,KPP_REAL,KPP_REAL [],KPP_REAL []); |
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| 10 | |
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| 11 | |
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| 12 | void FUNC_CHEM(int N,KPP_REAL T,KPP_REAL Y[NVAR],KPP_REAL P[NVAR]) |
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| 13 | { |
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| 14 | KPP_REAL Told; |
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| 15 | Told = TIME; |
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| 16 | TIME = T; |
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| 17 | Update_SUN(); |
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| 18 | Update_PHOTO(); |
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| 19 | Fun( Y, FIX, RCONST, P ); |
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| 20 | TIME = Told; |
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| 21 | } /* function fun ends here */ |
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| 22 | |
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| 23 | void JAC_CHEM(int N,KPP_REAL T,KPP_REAL Y[NVAR],KPP_REAL J[LU_NONZERO]) |
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| 24 | { |
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| 25 | KPP_REAL Told; |
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| 26 | Told = TIME; |
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| 27 | TIME = T; |
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| 28 | Update_SUN(); |
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| 29 | Update_PHOTO(); |
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| 30 | Jac_SP( Y, FIX, RCONST, J ); |
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| 31 | TIME = Told; |
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| 32 | } /* function jac_sp ends here */ |
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| 33 | |
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| 34 | |
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| 35 | INTEGRATE( KPP_REAL TIN, KPP_REAL TOUT ) |
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| 36 | { |
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| 37 | /* TIN - Start Time */ |
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| 38 | /* TOUT - End Time */ |
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| 39 | |
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| 40 | int INFO[5]; |
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| 41 | |
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| 42 | forfun = &FUNC_CHEM; |
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| 43 | forjac = &JAC_CHEM; |
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| 44 | INFO[0] = Autonomous; |
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| 45 | |
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| 46 | RODAS3( NVAR,TIN,TOUT,STEPMIN,STEPMAX,STEPMIN,VAR,ATOL,RTOL,INFO |
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| 47 | ,forfun ,forjac ); |
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| 48 | |
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| 49 | } |
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| 50 | |
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| 51 | |
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| 52 | |
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| 53 | int RODAS3(int N,KPP_REAL T, KPP_REAL Tnext,KPP_REAL Hmin,KPP_REAL Hmax, |
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| 54 | KPP_REAL Hstart,KPP_REAL y[NVAR],KPP_REAL AbsTol[NVAR],KPP_REAL RelTol[NVAR], |
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| 55 | int INFO[5],void (*forfun)(int,KPP_REAL,KPP_REAL [],KPP_REAL []), |
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| 56 | void (*forjac)(int,KPP_REAL,KPP_REAL [],KPP_REAL []) ) |
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| 57 | { |
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| 58 | /* |
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| 59 | Stiffly accurate Rosenbrock 3(2), with |
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| 60 | stiffly accurate embedded formula for error control. |
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| 61 | |
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| 62 | All the arguments aggree with the KPP syntax. |
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| 63 | |
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| 64 | INPUT ARGUMENTS: |
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| 65 | y = Vector of (NVAR) concentrations, contains the |
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| 66 | initial values on input |
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| 67 | [T, Tnext] = the integration interval |
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| 68 | Hmin, Hmax = lower and upper bounds for the selected step-size. |
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| 69 | Note that for Step = Hmin the current computed |
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| 70 | solution is unconditionally accepted by the error |
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| 71 | control mechanism. |
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| 72 | AbsTol, RelTol = (NVAR) dimensional vectors of |
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| 73 | componentwise absolute and relative tolerances. |
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| 74 | FUNC_CHEM = name of routine of derivatives. KPP syntax. |
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| 75 | See the header below. |
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| 76 | JAC_CHEM = name of routine that computes the Jacobian, in |
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| 77 | sparse format. KPP syntax. See the header below. |
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| 78 | Info(1) = 1 for autonomous system |
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| 79 | = 0 for nonautonomous system |
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| 80 | |
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| 81 | OUTPUT ARGUMENTS: |
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| 82 | y = the values of concentrations at Tend. |
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| 83 | T = equals Tend on output. |
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| 84 | Info(2) = # of FUNC_CHEM calls. |
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| 85 | Info(3) = # of JAC_CHEM calls. |
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| 86 | Info(4) = # of accepted steps. |
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| 87 | Info(5) = # of rejected steps. |
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| 88 | |
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| 89 | Adrian Sandu, March 1996 |
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| 90 | The Center for Global and Regional Environmental Research |
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| 91 | */ |
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| 92 | KPP_REAL K1[NVAR], K2[NVAR], K3[NVAR], K4[NVAR]; |
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| 93 | KPP_REAL F1[NVAR], JAC[LU_NONZERO]; |
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| 94 | KPP_REAL ghinv,uround,c43,x1,x2,ytol; |
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| 95 | KPP_REAL ynew[NVAR]; |
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| 96 | KPP_REAL H, Hold, Tplus,tau,tau1,tau2,tau3; |
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| 97 | KPP_REAL ERR, factor, facmax; |
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| 98 | int n,nfcn,njac,Naccept,Nreject,i,j,ier; |
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| 99 | char IsReject,Autonomous; |
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| 100 | |
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| 101 | |
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| 102 | |
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| 103 | /* Initialization of counters, etc. */ |
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| 104 | Autonomous = (INFO[0] == 1); |
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| 105 | uround = (double)1e-15; |
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| 106 | c43 = (double)(-8.e0/3.e0); |
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| 107 | H = MAX( (double)1e-8, Hstart ); |
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| 108 | Hmin = MAX(Hmin,uround*(Tnext-T)); |
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| 109 | Hmax = MIN(Hmax,Tnext-T); |
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| 110 | Tplus = T; |
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| 111 | IsReject = 0; |
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| 112 | Naccept = 0; |
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| 113 | Nreject = 0; |
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| 114 | nfcn = 0; |
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| 115 | njac = 0; |
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| 116 | |
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| 117 | |
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| 118 | /* === Starting the time loop === */ |
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| 119 | |
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| 120 | while(T<Tnext) |
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| 121 | { |
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| 122 | ten : |
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| 123 | Tplus = T + H; |
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| 124 | |
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| 125 | if ( Tplus > Tnext ) |
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| 126 | { |
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| 127 | H = Tnext - T; |
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| 128 | Tplus = Tnext; |
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| 129 | } |
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| 130 | |
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| 131 | (*forjac)(NVAR, T, y,JAC ); |
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| 132 | |
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| 133 | njac = njac+1; |
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| 134 | ghinv = (double)-2.0e0/H; |
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| 135 | for(j=0;j<NVAR;j++) |
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| 136 | JAC[LU_DIAG[j]] = JAC[LU_DIAG[j]] + ghinv; |
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| 137 | |
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| 138 | |
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| 139 | ier = KppDecomp (JAC); |
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| 140 | |
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| 141 | if ( ier != 0) |
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| 142 | { |
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| 143 | if( H > Hmin ) |
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| 144 | { |
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| 145 | H = (double)5.0e-1*H; |
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| 146 | goto ten; |
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| 147 | } |
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| 148 | else |
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| 149 | printf("IER <> 0 , H = %d", H); |
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| 150 | }/* main ier if ends*/ |
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| 151 | |
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| 152 | |
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| 153 | (*forfun)(NVAR , T, y, F1 ) ; |
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| 154 | |
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| 155 | |
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| 156 | /* ====== NONAUTONOMOUS CASE =============== */ |
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| 157 | |
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| 158 | if( Autonomous == 0) |
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| 159 | { |
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| 160 | tau = DSQRT( uround*MAX( (double)1.0e-5, dabs(T) ) ); |
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| 161 | (*forfun)(NVAR , T+tau , y ,K2 ); |
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| 162 | nfcn=nfcn+1; |
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| 163 | for(j=0;j<NVAR;j++) |
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| 164 | K3[j] = ( K2[j]-F1[j] )/tau; |
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| 165 | |
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| 166 | |
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| 167 | /* ----- STAGE 1 (NONAUTONOMOUS) ----- */ |
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| 168 | x1 = (double)0.5*H; |
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| 169 | |
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| 170 | for(j=0;j<NVAR;j++) |
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| 171 | K1[j] = F1[j] + x1*K3[j]; |
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| 172 | |
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| 173 | KppSolve (JAC, K1); |
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| 174 | |
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| 175 | /* ----- STAGE 2 (NONAUTONOMOUS) ----- */ |
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| 176 | |
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| 177 | x1 = (double)4.e0/H; |
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| 178 | |
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| 179 | x2 = (double)1.5e0*H; |
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| 180 | |
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| 181 | for(j=0;j<NVAR;j++) |
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| 182 | K2[j] = F1[j] - x1*K1[j] + x2*K3[j]; |
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| 183 | |
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| 184 | KppSolve (JAC, K2); |
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| 185 | }/* if nonautonomous case ends here */ |
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| 186 | |
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| 187 | |
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| 188 | /* ====== AUTONOMOUS CASE =============== */ |
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| 189 | else |
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| 190 | { |
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| 191 | /* ----- STAGE 1 (AUTONOMOUS) ----- */ |
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| 192 | for(j=0;j<NVAR;j++) |
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| 193 | K1[j] = F1[j]; |
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| 194 | |
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| 195 | KppSolve (JAC, K1); |
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| 196 | |
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| 197 | /* ----- STAGE 2 (AUTONOMOUS) ----- */ |
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| 198 | |
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| 199 | x1 = (double)4.e0/H; |
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| 200 | |
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| 201 | for(j=0;j<NVAR;j++) |
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| 202 | K2[j] = F1[j] - x1*K1[j]; |
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| 203 | |
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| 204 | KppSolve(JAC,K2); |
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| 205 | |
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| 206 | } /* else autonomous case ends here */ |
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| 207 | |
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| 208 | |
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| 209 | /* ----- STAGE 3 ----- */ |
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| 210 | |
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| 211 | for(j=0;j<NVAR;j++) |
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| 212 | ynew[j] = y[j] - 2.0e0*K1[j]; |
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| 213 | |
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| 214 | |
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| 215 | (*forfun)(NVAR , T+H , ynew ,F1 ); |
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| 216 | |
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| 217 | nfcn=nfcn+1; |
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| 218 | |
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| 219 | for(j=0;j<NVAR;j++) |
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| 220 | K3[j] = F1[j] + ( -K1[j] + K2[j] )/H; |
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| 221 | |
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| 222 | KppSolve (JAC, K3); |
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| 223 | |
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| 224 | |
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| 225 | |
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| 226 | /* ----- STAGE 4 ----- */ |
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| 227 | |
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| 228 | for(j=0;j<NVAR;j++) |
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| 229 | ynew[j] = y[j] - 2.0e0*K1[j] - K3[j]; |
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| 230 | |
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| 231 | (*forfun)(NVAR, T+H , ynew, F1 ); |
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| 232 | |
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| 233 | nfcn=nfcn+1; |
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| 234 | for(j=0;j<NVAR;j++) |
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| 235 | K4[j] = F1[j] + ( -K1[j] + K2[j] - c43*K3[j] )/H; |
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| 236 | |
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| 237 | KppSolve (JAC, K4); |
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| 238 | |
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| 239 | |
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| 240 | /* ---- The Solution --- */ |
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| 241 | for(j=0;j<NVAR;j++) |
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| 242 | ynew[j] = y[j] - (double)2.0e0*K1[j] - K3[j] - K4[j]; |
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| 243 | |
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| 244 | |
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| 245 | |
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| 246 | /* ====== Error estimation ======== */ |
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| 247 | |
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| 248 | ERR=(double)0.e0; |
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| 249 | |
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| 250 | for(i=0;i<NVAR;i++) |
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| 251 | { |
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| 252 | ytol = AbsTol[i] + RelTol[i]*dabs(ynew[i]); |
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| 253 | ERR = (double)(ERR + pow( K4[i]/ytol,2 )); |
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| 254 | } |
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| 255 | |
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| 256 | ERR = MAX( uround, DSQRT( ERR/NVAR ) ); |
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| 257 | |
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| 258 | /* ======= Choose the stepsize =============================== */ |
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| 259 | |
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| 260 | factor = (double)0.9/pow(ERR,1.e0/3.e0); |
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| 261 | |
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| 262 | if(IsReject == 1) |
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| 263 | facmax = (double)1.0; |
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| 264 | else |
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| 265 | facmax = (double)10.0; |
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| 266 | |
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| 267 | factor =(double) MAX( 1.0e-1, MIN(factor,facmax) ); |
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| 268 | |
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| 269 | Hold = H; |
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| 270 | H = (double)MIN( Hmax, MAX(Hmin,factor*H) ); |
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| 271 | |
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| 272 | |
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| 273 | /* ======= Rejected/Accepted Step ============================ */ |
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| 274 | |
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| 275 | if( (ERR>1) && (Hold>Hmin) ) |
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| 276 | { |
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| 277 | IsReject = 1; |
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| 278 | Nreject = Nreject + 1; |
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| 279 | } |
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| 280 | else |
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| 281 | { |
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| 282 | IsReject = 0; |
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| 283 | |
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| 284 | for(i=0;i<NVAR;i++) |
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| 285 | { |
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| 286 | y[i] = ynew[i]; |
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| 287 | } |
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| 288 | T = Tplus; |
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| 289 | Naccept = Naccept+1; |
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| 290 | } /* else should end here */ |
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| 291 | |
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| 292 | |
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| 293 | /* ======= End of the time loop =============================== */ |
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| 294 | |
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| 295 | |
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| 296 | }/* while loop (T < Tnext) ends here */ |
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| 297 | |
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| 298 | |
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| 299 | |
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| 300 | /* ======= Output Information ================================= */ |
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| 301 | |
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| 302 | INFO[1] = nfcn; |
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| 303 | INFO[2] = njac; |
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| 304 | INFO[3] = Naccept; |
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| 305 | INFO[4] = Nreject; |
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| 306 | |
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| 307 | return 0; |
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| 308 | |
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| 309 | |
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| 310 | } /* function rodas ends here */ |
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| 311 | |
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| 312 | |
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| 313 | |
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