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FindRoot failing in v8 on a system easily solvable in v7

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114743] FindRoot failing in v8 on a system easily solvable in v7
  • From: vasil michev <michev at gmail.com>
  • Date: Wed, 15 Dec 2010 07:50:58 -0500 (EST)

Consider the following input

eq1:=Block[{u1,u2,u3,u4},u1:=uX-2*NIntegrate[Cos[x]/(Exp[1/1.529266/
T*(uX*0.004559*(1-Cos[x])+uY*0.004559*(1-Cos[y])+uZ*0.012095*(1-
Cos[z]))]-1),{x,-\[Pi],\[Pi]},{y,-\[Pi],\[Pi]},{z,-\[Pi],\
[Pi]},PrecisionGoal->4, MaxPoints->15000000,Method ->
{"LocalAdaptive"}]/8/\[Pi]^3;
u2:=uY-2*NIntegrate[Cos[y]/(Exp[1/1.529266/T*(uX*0.004559*(1-Cos[x])
+uY*0.004559*(1-Cos[y])+uZ*0.012095*(1-Cos[z]))]-1),{x,-\[Pi],\[Pi]},
{y,-\[Pi],\[Pi]},{z,-\[Pi],\[Pi]},PrecisionGoal->4, MaxPoints-
>15000000,Method -> {"LocalAdaptive"}]/8/\[Pi]^3;
u3:=uZ-2*NIntegrate[Cos[z]/(Exp[1/1.529266/T*(uX*0.004559*(1-Cos[x])
+uY*0.004559*(1-Cos[y])+uZ*0.012095*(1-Cos[z]))]-1),{x,-\[Pi],\[Pi]},
{y,-\[Pi],\[Pi]},{z,-\[Pi],\[Pi]},PrecisionGoal->4, MaxPoints-
>15000000,Method -> {"LocalAdaptive"}]/8/\[Pi]^3;
u4:=1.529266-NIntegrate[1/(Exp[1/1.529266/T*(uX*0.004559*(1-Cos[x])
+uY*0.004559*(1-Cos[y])+uZ*0.012095*(1-Cos[z]))]-1),{x,-\[Pi],\[Pi]},
{y,-\[Pi],\[Pi]},{z,-\[Pi],\[Pi]},PrecisionGoal->4, MaxPoints-
>15000000,Method -> {"LocalAdaptive"}]/8/\[Pi]^3;
FindRoot[{u1,u2,u3,u4},{{uX,2,2.2},{uY,.5,.8},{uZ,1.5,2.5},{T,
0.01,0.1}},AccuracyGoal->5,PrecisionGoal->5]//Quiet]

In v7 I get

{uX->1.08147,uY->1.08147,uZ->2.08043,T->0.023582}


while in v8 I get NIntegrate::inumr errors. Help browser shows no
changes to FindRoot in v8 and I cant figure out whats failing. A quick
test shows that the equations dont have any undefined parameters

In[15]:= Block[{uX=1,uY=1,uZ=1,T=1},u1]
Out[15]= -69.385

so it must be FindRoot thats causing the problem. Any ideas?


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