Solving a System of Nonlinear Equations with FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg26749] Solving a System of Nonlinear Equations with FindRoot
• From: Morita Tomoyoshi <morita at gssm.otsuka.tsukuba.ac.jp>
• Date: Fri, 19 Jan 2001 02:14:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear MathGroup Reader,

I am a beginer user of Mathematica 4.0 on Windows. Would anyone please
help me with the following problem. Thank you very much in advance.

I am trying to solve a system of three to five nonlinear equations
using FindRoot.  The problem is either that it does not converge, that
a jacobian matrix is singular, or that numerical overflow/underflow
occurs.

I am using FindRoot with one starting value and (hence the algorithm
used here is damped Newton's method), but I have no accurate
information regarding this starting value which is probably the main
reason for getting such errors.  I only know that two of five unknown
variables are nonnegative, two of them take the value between 0 and 1,
and one of them takes a value between 0 and about 3, i.e.

0 < v,w
0 < x,y < 1
0 < z < 3

When the equations are of two unknown variables, I can simply
ContourPlot the two equations with contour \$B"*(B {0}\$B!!(Boption and
see where two graphs cross. But when the equations involve three
unknown variables, this is difficult even with ContourPlot3D as the
intersecting region of three surfaces is not clearly visible.

Could anyone please tell me how I can find the right starting values
for solving a system of three nonlinear equations involving three
unknown variables so that I can make the problem converge?

I also need to solve a system with four and five unknown variables.
This time, graphical approach cannot be used at all. Perhaps I need to
resort to a "binary seach" kind of approach albeit being very costly.
If anyone has information on how I can solve four and five equation
problem then please let me know.

(I also tried Solve instead of FindRoot but again without success. )

Thank you very much.