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MathGroup Archive 2007

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Re: FindRoot[] with mixed complex and real variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79650] Re: FindRoot[] with mixed complex and real variables?
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Wed, 1 Aug 2007 04:59:05 -0400 (EDT)

I made some syntax errors in my first reply.  This is corrected and note how I'm back-substituting the results into the equations to check the results.  Note that the the value calculated for x has an imaginary component on it.  So need to work with it more.

In[127]:=
solutionSet = FindRoot[{(x + I*y)*BesselJ[1, x + I*y]*
      BesselK[0, I*t] == I*t*BesselK[1, I*t]*
      BesselJ[0, x + I*y], (x + I*y)^2 - t^2 == -200 + I*s, 
    u*BesselJ[1, u]*BesselK[0, w] == w*BesselK[1, w]*
      BesselJ[0, u], u^2 + w^2 == g, u == x + I*y, w == I*t, 
    g == -200 + I*s}, {{x, 2.39}, {y, 0.17}, {t, 14.34}, 
    {s, 0.8}, {u, 2.39 + 0.17*I}, {g, -200 + 0.8*I}, 
    {w, 14.34*I}}, MaxIterations -> 50, 
   WorkingPrecision -> 15]
   
{(x + I*y)*BesselJ[1, x + I*y]*BesselK[0, I*t] - 
    t*BesselK[1, I*t]*BesselJ[0, x + I*y], 
   (x + I*y)^2 - t^2 - (-200 + I*s), 
   u*BesselJ[1, u]*BesselK[0, w] - w*BesselK[1, w]*
     BesselJ[0, u], u^2 + w^2 - g, u - (x + I*y), w - I*t, 
   g - (-200 + I*s)} /. solutionSet


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