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.