Wolfram Cloud Document

In[]:=

f[x_]:=1;F[x_]:=x;vec={XsI->0.5255185520,b0I->0.0008964905475,b0N->0.004110572847,bI->0.003593863837,bN->0.01943320750,e0II->0.001945817638,e0IN->0.01303529201,e0NI->0.008867450106,e0NN->0.05940423154,eI->0.005482919860,eN->0.02780877431,ebI->0.07684032836,ebN->0.3426896535,gI->0.02125849984,gN->0.01715919283,gbI->0.02330000000,gbN->0.01680000000,mm0->0.04719840288,p19I->0.6938220716,p19N->0.6956038476,sI->0.003224572183,sN->0.01725014096,t0->0.5164663938,uI->0.0007407941200,uN->0.002083827235,ubI->0.02163641199,ubN->0.03656271488,xI->0.3708143869};

In[]:=

r=0.0125;lN=0.5141*0.1295;lI=0.1265*0.1031;DI=0.1265;DN=0.5141;xN=1;

In[]:=

zN=((0.6*(1352.911208/1117.583451)*(1-Exp[((-4)*0.0125)])+400/1117.583451*Exp[((-4)*0.0125)])*(eN/(eN+bN+sN))+(1-(eN/(eN+bN+sN)))*400/1117.583451)/.vec;

In[]:=

zI=((0.6*1377.785804/1117.583451*(1-Exp[((-4)*0.0125)])+400/1117.583451*Exp[((-4)*0.0125)])*(eI/(eI+bI+sI))+(1-(eI/(eI+bI+sI)))*400/1117.583451)/.vec;gbN=0.0168;gbI=0.0233;ph=bN/(bN+bI)/.vec;lm=((gbN*ebN)/ubN)/.vec;profbN=2900.852468/1117.583451;profbI=3093.166523/1117.583451;l0=mm0*(t0)^(1-0.46)/.vec;FbN=Integrate[(1-F[x]),{x,a0N,1}];FbI=Integrate[(1-F[x]),{x,a0I,1}];avN=Integrate[x*f[x_]/(1-F[x]),{x,a0N,1}];avI=Integrate[x*f[x_]/(1-F[x]),{x,a0I,1}];eq1=(dN*(1-F[a0N])*lN-bN*(gN+dN*(1-F[a0N])))/.vec;eq2=(dN*(F[a0N]-F[asN])*(lN-bN)-seN*(gN+dN*(1-F[asN])))/.vec;

Integrate

:Integral of

1-x

does not converge on {a0N,1}.

Integrate

:Integral of

1-x

does not converge on {a0I,1}.

In[]:=

eq3=(dN*(F[asN]-F[auN])*(lN-bN-seN-eN)-suN*(gN+dN*(1-F[auN])+lm))/.vec;eq4=((lN-bN-seN)*lm-eN*(gbN+dN*(1-F[asN])+lm))/.vec;eq8=(dI*(1-F[a0I])*lI-bI*(gI+dI*(1-F[a0I])))/.vec;

In[]:=

eq9=(dI*(F[a0I]-F[asI])*(lI-bI)-seI*(gI+dI*(1-F[asI])))/.vec;eq10=(dI*(F[asI]-F[auI])*(lI-bI-seI-eI)-suI*(gI+dI*(1-F[auI])+XsI*lm))/.vec;eq11=((lI-bI-seI)*XsI*lm-eI*(gbI+dI*(1-(asI))+XsI*lm))/.vec;

In[]:=

eq21=((dN*sigN)/(r+gN)*FbN+cN-l0/(t0*(r+gN))*DeltN)/.vec;eq22=((dI*sigI)/(r+gI)*FbI+cI-l0/(t0*(r+gl))*DeltI)/.vec;eq23=(profbN-(sigN*avN+(gN+(l0/t0))/gN*DeltN-cN))/.vec;eq24=(profbI-(sigI*avI+(gI+l0/t0)/gI*DeltI-cI))/.vec;

In[]:=

eq25=(sigI*asI-(1377.785804/1117.583451-1/(r+gbI+XsI*lm)((gbI-gI)*(1377.785804/1117.583451-zI-dI*sigI*Integrate[(1-F[x])/(r+gI+XsI*lm+dI*(1-F[x])),{x,auI,asI}]))))/.vec;

In[]:=

eq26=(sigN*asN-(1352.911208/1117.583451-1/(r+gbN+lm)((gbN-gN)*(1352.911208/1117.583451-zN-dN*sigN*(Integrate[(1-F[x])/(r+gN+lm+dN*(1-F[x])),{x,auN,asN}])))))/.vec;eq27=(sigI*auI-zI)/.vec;eq28=(sigN*auN-zN)/.vec;

In[]:=

eqa=(seN-sN-suN)/.vec;eqb=(seI-sI-suI)/.vec;

In[]:=

FindRoot[{eq1,eq2,eq3,eq4,eq8,eq9,eq10,eq11,eq21,eq22,eq23,eq24,eq25,eq26,eq27,eq28,eqa,eqb},{{DeltI,0.7207275053},{DeltN,0.5288397662},{a0I,0.9873451479},{a0N,0.9920803385},{asI,0.9785782316},{asN,0.9812883008},{auI,0.5533906366},{auN,0.5870708},{dI,0.6389753755},{dN,0.8931406947},{sigI,0.1109169184},{sigN,0.3285473015},{suI,0.001710032852},{suN,0.003834686916},{cN,1},{cI,1},{seN,0.013415},{seI,0.00154}}]

Integrate

:Integral of

1-x

does not converge on {a0N,1}.

Integrate

:Integral of

1-x

does not converge on {a0I,1}.

Integrate

:Integral of

1-x

does not converge on {0.99208,1}.

General

:Further output of Integrate::idiv will be suppressed during this calculation.

NIntegrate

:Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small.

NIntegrate

:NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in x near {x} = {0.999999999999999999999999999999870851986456034765674304276446916690}. NIntegrate obtained 149.566 and 23.2473 for the integral and error estimates.

NIntegrate

:Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small.

NIntegrate

:NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in x near {x} = {0.999999999999999999999999999999793633981653460964059765148329266480}. NIntegrate obtained 149.561 and 23.2473 for the integral and error estimates.

FindRoot

:The function value -1.22567×

-12

,1.5379×

-8

,1.59997×

-7

,7.14951×

-8

,2.17239×

-13

,-8.89761×

-7

,-6.91727×

-6

,-2.10683×

-6

,-0.140183,1.00017-

0.0460998

0.0125+gl

,-48.0439,-15.7104,-1.10978,-0.889677,-0.304834,-0.172782,-0.00766983,-0.00339461 is not a list of numbers with dimensions {18} at {DeltI,DeltN,a0I,a0N,asI,asN,auI,auN,dI,dN,sigI,sigN,suI,suN,cN,cI,seN,seI} = {0.720728,0.52884,0.987345,0.99208,0.978578,0.981288,0.553391,0.587071,0.638975,0.893141,0.110917,0.328547,0.00171003,0.00383469,1.,1.,0.013415,0.00154}.

Out[]=

FindRoot[{eq1,eq2,eq3,eq4,eq8,eq9,eq10,eq11,eq21,eq22,eq23,eq24,eq25,eq26,eq27,eq28,eqa,eqb},{{DeltI,0.720728},{DeltN,0.52884},{a0I,0.987345},{a0N,0.99208},{asI,0.978578},{asN,0.981288},{auI,0.553391},{auN,0.587071},{dI,0.638975},{dN,0.893141},{sigI,0.110917},{sigN,0.328547},{suI,0.00171003},{suN,0.00383469},{cN,1},{cI,1},{seN,0.013415},{seI,0.00154}}]

In[]:=

FindRoot[{eq10,eq20,eq30,eq40,eq80,eq90,eq100,eq110,eq210,eq220,eq230,eq240,eq250,eq260,eq270,eq280,eqa0,eqb0},{{DeltI,0.72072},{DeltN,0.52883976},{a0I,0.98},{a0N,0.99208},{asI,0.978},{asN,0.98128},{auI,0.55339},{auN,0.5870},{dI,0.63897},{dN,0.893},{sigI,0.11091},{sigN,0.328547},{suI,0.001710},{suN,0.00383},{cN,1},{cI,1},{seN,0.013415},{seI,0.00154}}]

Integrate

:Integral of

1-x

does not converge on {a0N,1}.

Integrate

:Integral of

1-x

does not converge on {a0I,1}.

FindRoot

:In the first argument {0.066576(1-a0N)dN-0.0194332(0.0171592+(1+Times[2])dN)0,0.0471427(a0N-asN)dN-(0.0171592+(1+Times[2])dN)seN0,(asN-auN)dN(0.019334-seN)-(0.17462+(1+Times[2])dN)suN0,-0.0278088(0.174261+(1+Times[2])dN)+0.157461(0.0471427-seN)0,0.0130422(1-a0I)dI-0.00359386(0.0212585+(1+Times[2])dI)0,9,-0.366214+auIsigI0,-0.365663+auNsigN0,-0.0172501+seN-suN0,-0.00322457+seI-suI0} only some of the components are equations.

Out[]=

FindRoot[{eq10,eq20,eq30,eq40,eq80,eq90,eq100,eq110,eq210,eq220,eq230,eq240,eq250,eq260,eq270,eq280,eqa0,eqb0},{{DeltI,0.72072},{DeltN,0.52884},{a0I,0.98},{a0N,0.99208},{asI,0.978},{asN,0.98128},{auI,0.55339},{auN,0.587},{dI,0.63897},{dN,0.893},{sigI,0.11091},{sigN,0.328547},{suI,0.00171},{suN,0.00383},{cN,1},{cI,1},{seN,0.013415},{seI,0.00154}}]