How to solving and plot only one non-linear equation with two or one variables without using ezplot

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Tak Yeung POON
Tak Yeung POON 2020-2-14
评论： darova 2020-2-17
I want to solve and plot one non linear equation with two variables k and f, the equation is shown here, where k varies from 0 to 1. The other algebras are given.
(((2*pi*f).^2)/((2*pi*fv).^2)-1)*((2-(((2*pi*f).^2)/((k.^2)*(cs.^2))).^2)-4*((1-(((2*pi*f).^2)/((k.^2)*(cs.^2)))).^0.5)*((1-(((2*pi*f).^2)/((k.^2)*(cl.^2)))).^0.5)-m*(((2*pi*f).^4)/(A*(cs.^4)*den*(k.^3)))*((1-(((2*pi*f).^2)/((k.^2)*(cl.^2)))).^0.5))=0
For every k value, there are more than one possible solutions for f value, where the f value can be in form complex number and is limited from 0 to 20.
However, it gives 'The input to FSOLVE should be either a structure with valid fields or consist of at least two arguments.' after running the command.
Apart from that, i actually want to plot a continous function rather than scattering the point if it is possible. I don't want to use ezplot because the plot is not correct. Thankyou
clc
clear all
syms k f
cs = 121;
cl = 227;
A = (1.3^2)*(3^0.5)/2;
den = 1300;
m = 6700;
fv = 4.9;
k=0:0.01:1;
fun = @(f) ((2*pi*f).^2)/((2*pi*fv).^2)-1)*((2-(((2*pi*f).^2)/((k.^2)*(cs.^2))).^2)-4*((1-(((2*pi*f).^2)/((k.^2)*(cs.^2)))).^0.5)*((1-(((2*pi*f).^2)/((k.^2)*(cl.^2)))).^0.5)-m*(((2*pi*f).^4)/(A*(cs.^4)*den*(k.^3)))*((1-(((2*pi*f).^2)/((k.^2)*(cl.^2)))).^0.5)));
fsolve(fun, [0, 20])
scatter(k,f)
ylim([0 20]);
xlim([0 1])

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回答（1 个）

darova
darova 2020-2-14
Numerical way
[K,F] = mehsgrid(-10:10);
Z = your_function
contour(K,F,Z,[0 0]) % contour at 0 level
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