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

• To: mathgroup at smc.vnet.net
• Subject: [mg108815] Find the solution of a system of two nonlinear, complicated equations
• From: "Christian Schneider" <kofferpc at gmx.net>
• Date: Thu, 1 Apr 2010 06:02:21 -0500 (EST)

```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}.

I think mathematica is telling me that the iterations or the starting points
need to be changed. I tried to do that, but always end up with that error
messages.

I have a set of two equations with two variables and two parameters each,
and I want to solve the two variables of the set.

The variables of the two equations are: sigmabare, dmu

The two parameters per equation are

for equation1: epsilon1, c01

for equation2: epsilon2, c02

The complete syntax as plain text is:

FindRoot[{c01*6.022*10^(23) ==

Abs[sigmabare/(2*(437*10^(-12))*3*(1.602*10^(-19)))]*

Exp[(-(4.11641*10^(-21))*(1.65*(1/(4*(4.11641*10^(-21))*

epsilon1*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^\

3*sigmabare/3.141592654)^(1/2)) -

2.61*(1/(4*(4.11641*10^(-21))*

epsilon1*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^\

3*sigmabare/3.141592654)^(1/2))^(1/4) +

0.26*Log[

1/(4*(4.11641*10^(-21))*

epsilon1*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^\

3*sigmabare/3.141592654)^(1/2)] + 1.95))/((4.11641*10^(-21)))]*

Exp[dmu/((4.11641*10^(-21)))]/(6.022*10^(23)) /.

c01 -> {0.5*10^(-5)} /. epsilon1 -> {54} ,

c02*6.022*10^(23) ==

Abs[sigmabare/(2*(437*10^(-12))*3*(1.602*10^(-19)))]*

Exp[(-(4.11641*10^(-21))*(1.65*(1/(4*(4.11641*10^(-21))*

epsilon2*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^3*

sigmabare/3.141592654)^(1/2)) -

2.61*(1/(4*(4.11641*10^(-21))*

epsilon2*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^3*

sigmabare/3.141592654)^(1/2))^(1/4) + 0.26*Log[

1/(4*(4.11641*10^(-21))*

epsilon2*(8.854*10^(-12)))*((1.602*10^(-19))^3*3^3*

sigmabare/3.141592654)^(1/2)] +

1.95))/((4.11641*10^(-21)))]*

Exp[dmu/((4.11641*10^(-21)))]/(6.022*10^(23))} /.

c02 -> {1*10^(-5)} /.

epsilon2 -> {78}, {{sigmabare, 0.2}, {dmu, 4}}]

Sorry for this mess of equations.

Has somebody an idea where I am going wrong and how to solve this?