fixed point in a function of two variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg28336] fixed point in a function of two variables*From*: "Higinio Ramos" <higra at gugu.usal.es>*Date*: Thu, 12 Apr 2001 02:18:01 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I want to obtain the fixed point of a process that is supposed to be convergent. The Mathematica function FixedPoint also works with functions of two variables.Even I have added a test function so that it finalizes when the difference is minor than 0.001. But I must abort the process because it enters a curl and there are two points that are repeated indefinitely as it is observed with NestList. Does anybody know how I can obtain the fixed point? Thanks for your help. 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; 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]] \!\(\[Mu][T_] 10\^\(\(-3\) + 10\^\(\(-0.0565317247667186`\) + 0.005230675060360752`\ \ \((120 - T)\)\)\)\) 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], \[Mu][newT[Pwf]]}) test1[x_, y_] := Abs[x[[1]] - y[[1]]] < .0001 {Tfinal, \[Mu]final} = FixedPoint[fonRep, {Ta, \[Mu][Ta]}, SameTest -> test1] In[105]:= NestList[fonRep, {Ta, \[Mu][Ta]}, 10] Out[105]= {{20, 0.846763}, {67213.4, 0.00100000000000000000000000000000000000000000000000000000000000000000000 0\ 0000000000000000000000000000000000000000000000000000000000000000000000000 00000\ 0000000000000000000000000000000000000000000000000000000000000000000000000 00000\ 0000000000000000000000000000000000000000000000000000000000000000000000000 00000\ 000000000000000000000000000000000000000000000002300310171744}, {99.3532, 0.0133601}, {1080.17, 0.00100002}, {99.3548, 0.0133594}, {1080.12, 0.00100002}, {99.3548, 0.0133594}, {1080.12, 0.00100002}, {99.3548, 0.0133594}, {1080.12, 0.00100002}, {99.3548, 0.0133594}}