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~