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Solving differential equations in the complex plane
Posted:
Oct 5, 2009 7:39 AM


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 RungeKutta 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.



