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Re: Find the solution of a system of two nonlinear, complicated equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108832] Re: Find the solution of a system of two nonlinear, complicated equations
  • From: Peter Pein <petsie at dordos.net>
  • Date: Fri, 2 Apr 2010 05:21:14 -0500 (EST)
  • References: <hp1ufs$6d4$1@smc.vnet.net>

On 01.04.2010 13:02, Christian Schneider wrote:
> Dear members of the mathgroup email group,
>
> I have serious difficulties in solving the following problem in Mathematica
> v.7 and would very grateful if anyone could give me a helping hand with
> that.
>
> I want to solve a system of two nonlinear equations. Unfortunately the
> equations are rather bulky. I've tried to use FindRoot for this problem, but
> I get three error messages:
>
> General::ovfl : Overflow occurred in computation
>
> General::ovfl : Overflow occurred in computation
>
> FindRoot::nlnum : The function value {Overflow[], Overflow[]} is not a list
> of numbers with dimensions {2} at {sigmabare, dmu}={0.2, 4}.
...
> Has somebody an idea where I am going wrong and how to solve this?
>
>
>
> Thanks a lot in advance for your help,
>
>
>
> Chris
>

Hi Chris,

just a remark: use "equation"/.{c01->.5/10^5,epsilon->54}, because this 
gives an equation, while equation/.c01->{.5/10^5}/.epsilon->{54} leaves 
you with a list of a list of an eqn:
  a==b+c/.b->{1}/.c->{Pi}
    a=={{1+Pi}}

I replaced 3.141592654 with Pi and put the equations into a variable 
named eqns.
Then I mapped a Log onto both sides of both equations, replaced a==b by 
a-b and did a FullSimplify on the result:
eqns=FullSimplify[Subtract@@@Map[Log,eqns,{2}]//PowerExpand]
this led to
{37.0414516164153 - 2.429301260078564*^20*dmu - 
5.769493817846427*sigmabare^(1/8) + 39.39787193680568*Sqrt[sigmabare] + 
0.13000000000000003*Log[sigmabare] -
    1.*Log[Abs[sigmabare]], 37.63899035414267 - 
2.429301260078564*^20*dmu - 5.262747112219505*sigmabare^(1/8) + 
27.275449802403934*Sqrt[sigmabare] +
    0.13000000000000003*Log[sigmabare] - 1.*Log[Abs[sigmabare]]}
for which FindRoot gives
In[2]:= FindRoot[eqns,{{sigmabare,.2},{dmu,4}}]
Out[2]= {sigmabare->0.00502108,dmu->1.70676*10^-19}

hth,
Peter


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