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Re: [Help-gsl] finding roots, solving ODEs and numerical integration of
Re: [Help-gsl] finding roots, solving ODEs and numerical integration of complex functions
Fri, 05 Aug 2011 07:38:17 +0200
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.