Tc0=1;​​rg=Rationalize[0.0575630,0];​​ratio=Rationalize[0.1,0];​​Γ0=rg2πTc0;​​Γp=ratioΓ0;​​Γt=Γ0+Γp;​​nMax=10000;​​Ts=Rationalize[1.02514,0];​​Tc=Rationalize[0.942668,0];​​​​(*Fourthorderalgebraicequationforgwn*)​​{sol1[n_,Mag_,Tcm_],sol2[n_,Mag_,Tcm_],sol3[n_,Mag_,Tcm_],sol4[n_,Mag_,Tcm_]}=gwn/.Solve[1/gwn^21+Mag^2/((2n+1)PiTcm+2Γtgwn)^2,gwn];
In[]:=
(*EquationforTcm*)​​sumArg4Tcm[n_,Mag_,Tcm_]=2PiTcm(2n+1)PiTcm(sol4[n,Mag,Tcm]-1)/((2n+1)PiTcm+2Γp)/((2n+1)PiTcm+2Γpsol4[n,Mag,Tcm]);​​target1Tcm[Tcm_]=Log[Tcm/Tc]+PolyGamma
1
2
+
Γp
πTcm
-PolyGamma
1
2
+
Γp
πTc
;
In[]:=
myTrial4Tcm[Mag_?NumericQ,Tcm_?NumericQ]:=Parallelize[Sum[sumArg4Tcm[n,Mag,Tcm],{n,0,nMax}]]//Chop;​​
In[]:=
(*EquationforMag*)​​sumArg4Mag[n_,Mag_,Tcm_]=2PiTcm(2n+1)PiTcm(sol4[n,Mag,Tcm]-1)/((2n+1)PiTcm+2Γt)/((2n+1)PiTcm+2Γtsol4[n,Mag,Tcm]);​​target1Mag[Tcm_]=Log[Tcm/Ts]+PolyGamma
1
2
+
Γt
πTcm
-PolyGamma
1
2
+
Γt
πTs
;​​myTrial4Mag[Mag_?NumericQ,Tcm_?NumericQ]:=Parallelize[Sum[sumArg4Mag[n,Mag,Tcm],{n,0,nMax}]]//Chop;
In[]:=
AbsoluteTiming[FindRoot[{Re[myTrial4Tcm[Mag,Tcm]-target1Tcm[Tcm]],Re[myTrial4Mag[Mag,Tcm]-target1Mag[Tcm]]},{Mag,2.28},{Tcm,0.235}​​]]
FindRoot
:The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances.
Out[]=
{346.283,{Mag2.26353,Tcm0.241149}}
​