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