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MathGroup Archive 1994

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Re: solve complex ODE's

  • To: mathgroup-adm at christensen.cybernetics.net
  • Subject: Re: solve complex ODE's
  • From: keiper
  • Date: Wed, 26 Oct 1994 12:27:54 -0500

	> I am interested in Mma routines that solve complex ODE's.
	> Is there any at all? Another programs are welcome too.


You can use NDSolve, but you have to reparameterize the independent
variable to be real.  Thus, instead of

	NDSolve[{y'[z] == y[z], y[1+I] == 1}, y[z], {z, 1+I, 2+3I}]

you have to think of y as a function of t:  yz[t] == y[z[t]]:

	NDSolve[{yz'[t] == yz[t] z'[t], yz[0.0] == 1,
		z'[t] == ((2+3I) - (1+I))/(1-0), z[0.0] == 1+I},
		{yz[t], z[t]}, {t, 0.0, 1}]

where I have chosen the reparameterization z[t] to be linear.
The only restriction on the reparameterization would be that you
want to be able to invert it to get a result y[z] == yz[t[z]], where
t[z] is the inverse of z[t].

Jerry B. Keiper
keiper at wri.com
Wolfram Research, Inc.





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