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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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