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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: [mg79643] Re: FindRoot[] with mixed complex and real variables?
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Wed, 1 Aug 2007 04:55:25 -0400 (EDT)

Ok, ok.  I was wrong.  How about coding it as 7 variables in 7 unknowns (the two equations in terms of u, v and w, then the same two equations in terms x, y, t and s (that's 4, then these three:

u=x+iy
w=it
g=-200+is

Alright, that's seven.  Then use FindRoot with your starting values:

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, 0.8}, {t, 14.34}, 
   {s, 0.8}, {u, 2.39 + 0.17*I}, {g, -200 + 0.8*I}, 
   {w, 14.34*I}}]

when I do that, I get the following solutions:

{x -> -2.389999999999996 + 1.7419722275807886*^-15*I, 
  y -> 0.7999999999999983 + 3.775812800225189*^-15*I, 
  t -> 14.34 + 8.01608452040757*^-24*I, 
  s -> 0.8 + 4.257789892107953*^-22*I, u -> 2.39 + 0.17*I, 
  g -> -200. + 0.8*I, w -> -8.016084539066267*^-24 + 14.34*I}

> Yes -- besides the two initial complex-valued
> equations, there are the 
> two real constraints:   Re[w]==0  and  Re[g]==(a
> fixed & stated value).  
> 
> So, there's enough info to solve the problem, and I
> can indeed get 
> answers in other ways.  My problem is how to get this
> info into 
> FindRoot[].
>


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