Numerical Solution
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Hi everybody,
I have an equation which is:
i*q=k*sin(q)
I need to use the matlab to find its roots. I want to set a specific values of k like (0.25, 0.5, 1, 2, 3) and find the values of q each time. Thanks in advance folks.
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Teja Muppirala
el 22 de Jun. de 2012
Ok, your "q" will have an imaginary component, so you cannot use fzero directly. You can, however, solve it using fsolve, where you treat q as a 2-element vector containing the real and imaginary parts.
k = 4;
f = @(q) 1i.*[q(1) + 1i*q(2)]-k.*sin([q(1) + 1i*q(2)]);
x0 = [2; 0.5]
fsolve(@(q) norm(f(q)), x0)
This finds a zero at roughly [3; -0.7]. But since there are multiple minima, the result will depend on the initial conditions.
Note that you can make a plot of f, to visually see roughly where the zeros are. This will help you choose initial conditions.
k = 4;
f = @(q1,q2) 1i.*[q1 + 1i*q2]-k.*sin([q1 + 1i*q2]);
[Q1,Q2] = ndgrid(-10:.2:10);
surf(Q1,Q2, log(abs(f(Q1,Q2))));
1 comentario
Teja Muppirala
el 22 de Jun. de 2012
Just as a note, instead of fsolve, fminsearch would work just as well.
Más respuestas (2)
Walter Roberson
el 29 de Mayo de 2012
fsolve() or fzero() or one of the minimizers.
2 comentarios
Walter Roberson
el 22 de Jun. de 2012
fsolve() cannot deal directly with complex functions. Please see
http://www.mathworks.com/matlabcentral/answers/41458-fsolve-and-complex-solution
Image Analyst
el 21 de Jun. de 2012
Funny, I just copied the example from the help, and never having used fzero before myself, got the answer in about 5 seconds:
i=2 % Pick some sample values.
k=4
f = @(q)i.*q-k.*sin(q); % Replace example equation with Abdulaziz's
% Then find the zero near 2:
z = fzero(f,2)
z = 1.8955
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