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## Re: [Help-gsl] finding roots, solving ODEs and numerical integration of

 From: Владимир Дрынкин Subject: Re: [Help-gsl] finding roots, solving ODEs and numerical integration of complex functions Date: Fri, 5 Aug 2011 12:59:13 +0400

```a) Do you mean, that i should split my complex function f(z) into
system of two functions, returning real(f(z)) and imag(f(z)) and solve
this system using multidimensional routines? Hmm... It seems like a
very good idea :) Thanks a lot!!

b) I'm not so good at complex analysis, but i think, that the
separation of real and imaginary parts may be useful for my task. I'll
try this way. Thanks!

c) Ok, i'll try to do it.

Thanks a lot, Marco!
Thanks, GSL team =)

> Владимир Дрынкин wrote:
>
>> a) how can i find complex roots of nonlinear and nonpolynomial
>> function? The example of this function is described here:
>> http://lists.gnu.org/archive/html/help-gsl/2007-04/msg00046.html but
>
> Separate  the  real  and   imaginary  parts  and  apply  the
> multidimensional root finders?
>
>> b) how can i  numerically integrate the function returning
>> complex  numbers (for  example,  gsl_complex_tan)? i  have
>> read  the gsl  reference, but  it seems  like there  is no
>> appropriate algorithms.
>
> You have to decide  what "integrating" means in your context
> for functions  in the complex field,  then probably separate
> the  real and  imaginary parts  and apply  the  algorithm to
> them.  For some possible meanings of "integrating" it may be
> that, indeed, there is no algorithm in GSL.
>
>> c) if i have an  ODE like dy/dz=f(z) and the function f(z)
>> returns complex  numbers, how can i  solve it numerically?
>> what algorithm should i use?
>
> You have to  split the single equation in  the complex field
> in the two equations for  the real and imaginary parts, each
> of which uses real numbers.
>
> TIA
> --
> Marco Maggi
>

```