plot a nonlinear equation using FSOLVE Routine in matlab

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mohammaddmt 2019-5-7

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评论： mohammaddmt 2019-5-8

Hello all;

I have a nonlinear equation like this :

in this equation :

and:

f is frequency and is between:

I want to plot

vs. f.

there is from an article in which the author said she used FSOLVE Routine in matlab to solve this. and at last she derived this figure:

in which the real and imaginary parts of ky are considered.

Mr. John D'Errico said FSOLVE just gives the real part of a solution.

so how the author of the article solved the equation for both the real and the imaginary part of ky?

Just give me a hint, I will do the rest.

Mohammad

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Torsten 2019-5-8

编辑：Torsten 2019-5-8

Just out of interest:

Why does the graphic show Im(ky) for 0<f<10 and Re(ky) for 10<f<20 ? Is there a physical reason for this ?

And why does the y-axis show real values for ky if ky itself is complex-valued ? Does it mean that the y-axis shows Re(ky) resp. Im(ky) depending on the region for f ?

And what is eta(ky) ?

mohammaddmt 2019-5-8

the real part of ky is zero for the first and the third part and in the middle, the imaginary part of ky is zero. so the y xis shows real and imaginary values of ky.

BTW I just solved the problem. I had to break the equation to two equivalent equations by considering the real and imaginary parts of ky. so if we have a particular f, that means we have a particular k and then we have a solution for a system of nonlinear equations. this way, the fsolve could be used to solve the problem .

eta(ky) is just another approximation which is: