ghasem
Posts:
72
Registered:
4/13/13


Re: how find a relation between unknowns in this equation?please
Posted:
May 8, 2013 8:43 PM


"Nasser M. Abbasi" wrote in message <kmeoa2$uao$1@speranza.aioe.org>... > On 5/8/2013 4:41 PM, ghasem wrote: > > "ghasem " <shaban_sadeghi@yahoo.com> wrote in message <kmeg52$jkt$1@newscl01ah.mathworks.com>... > >> Hi. > >> I have a nonlinear equation including bessel functions with complex argument,as following: > >> > >> my_equation=(w*sqrt(k^2100)*besseli(1,sqrt(k^2 w))*besselk(0,sqrt(k^2100))+... > >> besselk(1,sqrt(k^2100))*besseli(0,sqrt(k^2 w))); > > ============== > > I'm sorry,I forgot that tell above equation is =0.i.e: > > I have equation of f(real(k),imag(k),w)=0; % f = my_equation > > that: > > my_equation=(w*sqrt(k^2100)*besseli(1,sqrt(k^2 w))*besselk(0,sqrt(k^2100))+... > > besselk(1,sqrt(k^2100))*besseli(0,sqrt(k^2 w))) =0 > > please direct me... > > thanks > > ghasem > > > > I guess you have 4 options to solve your bessel function > equation. > > 1) solve the real and the imaging parts as was talked about before > and combine result. > > 2) use symbolic solve(): > > w=99; syms k; > my_equation=(w*sqrt(k^2100)*besseli(1,sqrt(k^2 w))*besselk(0,sqrt(k^2100))+... > besselk(1,sqrt(k^2100))*besseli(0,sqrt(k^2 w))); > solve(my_equation,k) > >  0.00023072214491381421450643003838304  2.1259310417079225152113020224253*i > > 3) Use a computer algebra system that supports root finding with > complex numbers: > >  > Clear[a, b, k]; > w = 99; > r = Sqrt[k^2  100]; > eq = w r BesselI[1, r] BesselK[0, r] + BesselK[1, r] BesselI[0, r]; > FindRoot[eq == 0, {k, 0.01 + 2 I}] > {k > 0.000263968 + 1.87608 I} > > FindRoot[eq == 0, {k, 0.01 + 2 I}] > > FindRoot[eq == 0, {k, 100}] > {k > 7.1247 + 0.000100538 I} > > FindRoot[eq == 0, {k, 99 + 200 I}] > {k > 9.99814 + 0.0014217 I} >  > > 4) use a matlab toolbox that allows complex root finding > such as Chebfun and others like it. You can search fileexchange > on this topic. > > good luck, > > Nasser ========================================= thank you very much Mr Abbasi... I will try again with chebfun... best wishes... ghasem

