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Can I solve this system of nonlinear equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125217] Can I solve this system of nonlinear equations?
  • From: Andy <andy732a at gmail.com>
  • Date: Wed, 29 Feb 2012 07:25:38 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I'm dealing with systems of nonlinear equations that have 8 equations
and 8 unknowns.  Here's an example:

Solve[{(((c - a)/0.002) - (0.995018769272803 + h*b)) == 0,
  (((d - b)/0.002) - (0.990074756047929 + h*c)) == 0,
  (((e - c)/0.002) - (0.985167483257382 + h*d)) == 0,
  (((f - d)/0.002) - (0.980296479563062 + h*e)) == 0,
  (((g - e)/0.002) - (0.975461279165159 + h*f)) == 0,
  (((-1*e + 8*d - 8*b + a)/(12*0.001)) - (0.990074756047929 + h*c)) ==
0,
  (((-1*f + 8*e - 8*c + b)/(12*0.001)) - (0.985167483257382 + h*d)) ==
0,
  (((-1*g + 8*f - 8*d + c)/(12*0.001)) - (0.980296479563062 + h*e)) ==
0}, {a, b, c, d, e, f, g, h}]

Whenever I try this, Mathematica 7 just returns the empty set {}.  How
can I tell if this is unsolvable?  Shouldn't I at least be able to get
a numerical approximation with NSolve?  I've tried using stochastic
optimization to get approximate answers but every method gives poor
results, and that's why I would like to at least approximately solve
this if possible.  Thanks very much for any help~



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