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Topic: Solving differential equations in the complex plane
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André Hautot

Posts: 18
Registered: 12/8/04
Solving differential equations in the complex plane
Posted: Oct 5, 2009 7:39 AM
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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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