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Solving differential equations in the complex plane

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103768] Solving differential equations in the complex plane
  • From: Andre Hautot <ahautot at ulg.ac.be>
  • Date: Mon, 5 Oct 2009 07:39:48 -0400 (EDT)

Hi !
How can I solve an ordinary differential equation of order n in the 
complex plane following a prescribed contour ?
I can of course write my own Runge-Kutta package but is there a quickest 
way to do that (maybe NDSolve but how to define the contour ??) ?

Example : NDSolve[{y'[x] == Exp[y[x]], y[1] == 1}, y, {x, 1, 3}]
fails because of a singularity in x=1+1/e.
However integrating the ODE following a path which avoids the 
singularity should be possible eventually leading to a multivalued function.

Thanks for a hint.



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