RE: fixed point in a function of two variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg28438] RE: [mg28336] fixed point in a function of two variables*From*: "Higinio Ramos" <higra at gugu.usal.es>*Date*: Thu, 19 Apr 2001 03:26:26 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

When I receive an e-mail of the MathGroup the first thing that I do is to reproduce the situation that is indicated. I have to apologize because after receiving the message of Tomas Garza I have tried to do the operations that I sent and I have had problems with [ Mu][T _ ] etc. [ Mu][T _ ] was a function that measure the viscosity of a fluid (oil) and the two following functions newT[Pwf2 _ ] and fonRep[{T _, mu _ } ] were to obtain the final temperature of working of an axis that turn within a cylinder and have a lubrication by oil. fonRep[{T _, mu _ } ] is a function that have a point fix but there are problems in calculate it because after applying the Mathematica function FixedPoint this enter in a cycle and is impossible to obtain. I show the problem again changing the name [ Mu][T _ ] by vis[T_]: r = 0.05; b0 = 0.03 10^(-3); b1 = 0.066 10^(-3); n = 500; T0 = 80; Ta = 20; U = 2 Pi n r/60; PPi = Pv - 10^5; e = (b1 - b0)/2; R = r + (b0 + b1)/2; b = Sqrt[R^2 - e^2 Sin[t]^2] + e Cos[t] - r; sol = Solve[ 6 r mu U NIntegrate[1/b^2, {t, 0, 2Pi}] - r 12 mu Q NIntegrate[1/b^3, {t, 0, 2Pi}] == 0, Q]; Q = Q /. sol[[1]] Out[9]= 0.0000504476 vis[T_] := (10^(-3))*10^(10^(((Log[10, Log[10, 200]] - Log[10, Log[10, 7.55]])(120 - T))/(120 - 40) + Log[10, Log[10, 7.55]])); newT[Pwf2_] := If[2 r <= 0.1, (-Pwf2 + 20(35 + 30 r)10^(-3) Ta)/(20(35 + 30 r)10^(-3)), (-Pwf2 + 20(25 + 40 r^2 10^3)10^(-3) Ta)/(20(25 + 40 r^2 10^3)10^(-3))]; fonRep[{T_, mu_}] := (\[Tau][t_] := -4 mu U /b + 6 mu Q/b^2; M = r^2NIntegrate[\[Tau][t], {t, 0, 2Pi}]; Pwf = M U/r; {newT[Pwf], vis[newT[Pwf]]}); And the problem: FixedPoint[fonRep,{Ta,vis[Ta]}] and why: NestList[fonRep, {Ta, vis[Ta]}, 20] Despite that, I think I have solved the problem: like the viscosity depends also of the temperature T, I have expressed the function fonRep only as function of this temperature T. fonRep[T_] := (\[Tau][t_] := -4 vis[T] U /b + 6 vis[T] Q/b^2; M = r^2NIntegrate[\[Tau][t], {t, 0, 2Pi}]; Pwf = M U/r; newT[Pwf]) I obtain the interpolation function of a collection of point of this function fonRep[T] and making the intersection with the diagonal we see that there is only one fixed point: int = Interpolation[Table[{T, fonRep[T]}, {T, Ta, 300, 5}]]; Plot[int[T], {T, Ta, 300}]; finalT = FindRoot[int[T] == T, {T, Ta}]; T /. finalT Thanks to everybody that answered. Higinio Ramos