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Topic: how solve a equation including bessel functions?
Replies: 3   Last Post: Feb 7, 2014 8:15 AM

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Alan Weiss

Posts: 1,430
Registered: 11/27/08
Re: how solve a equation including bessel functions?
Posted: May 3, 2013 8:53 AM
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On 5/2/2013 6:59 PM, ghasem wrote:
> hi.
> I want to find all of zeros following equation:
> t0*besseli(1,t1) * besselk(0,t0) + t1 * besselk(1 ,t0) * besseli(0,t1)
> = 0
> where:
> k0 is real constant and known.
> t0 and t1 are in terms of k:
> t1 = sqrt(k^2-?r*k0^2) t0 = sqrt(k^2-k0^2) k is unknown complex number
> ( k = k1 +j k2 )
> besseli and besselk are modified bessel functions of first and second
> type.
> in above equation,only unknown is k .
> now, i want to find zeros of above equation,i.e find " k " values.
> by using of solve command only one of the zeros are found.
> i can not use from fzero command,because I don't have any guess point
> that is imaginary(k) = k2 =0.
> i don't know how find all of zeros in this equation.
> this equation is a dispersion relation.
> is there someone who help me?
> ghasem

You can use fsolve from Optimization Toolbox. Take the real and complex
parts of everything in sight so that the arguments are (k1,k2) and the
result is (freal,fcomplex), where f is the value of the left-had side of
your equation. Start fsolve at a whole lot of different points and
gather the solutions.

Alan Weiss
MATLAB mathematical toolbox documentation

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