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MathGroup Archive 2010

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root finding routine

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113600] root finding routine
  • From: nt <sagittarius5962 at gmail.com>
  • Date: Thu, 4 Nov 2010 03:59:29 -0500 (EST)

Hi,

I'm trying to find the roots of the following fourth order equation in
w and k:

eq = w^4 -a w^2 k +b  k^4 /. k -> (kx^2 + ky^2)^0.5;

eq1 = eq /. {w -> w1, kx -> k1x, ky -> 0};
eq2 = eq /. {w -> w2, kx -> k2x, ky -> k2y};
eq3 = eq /. {w -> w3, kx -> k3x, ky -> k3y};

given w1 and teta, and that  the roots for w and k should satisfy
these linear conditions:

sol = FindRoot[{eq1 == 0, eq2 == 0, eq3 == 0, k3x == k1x - k2x,
   w3 == w1 - w2, k2y == k2x*Tan[teta], k3y == -k2y}, {w1,
   2.767}(*{k1x,
  10}*), {k2x, .81}, {k2y, -.5}, {k3x, 1.83}, {k3y, -10}, {w3,w1/2},
{w2,w1/2}]

The above system has four sets of solutions.The findroot routine gives
one of the acceptable sets of solutions but could not get the others.
I played alot with the initial values but it seems that the routine
cannot converge to the other roots even if I put the actual other root
values as the initial guess. I would appreciate it if anyone could
provide helpful suggestions on the problem.

Thanks



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