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

[Marco Maggi]

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
> no one has answered this thread :(

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