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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 =)
best regards, Vladimir.
2011/8/5 Marco Maggi <address@hidden>:
> 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
>