Numerical Solution

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.

Answer 1

[Teja Muppirala]

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))));

[Teja Muppirala]

Just as a note, instead of fsolve, fminsearch would work just as well.

Answer 2

[Walter Roberson]

fsolve() or fzero() or one of the minimizers.

[Abdulaziz]

Hi Walter,

Tried, tried, and tried, but totally confused. Could you please help me applying fsolve() or fzero() in my case

Thanks again

[Walter Roberson]

fsolve() cannot deal directly with complex functions. Please see

http://www.mathworks.com/matlabcentral/answers/41458-fsolve-and-complex-solution

Answer 3

[Image Analyst]

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

[Abdulaziz]

hi,

I would like to thank you for helping me, but my i here is not a number it represents a complex number or component. Tried what you did, and this what I got:

k=4

f = @(q)1i.*q-k.*sin(q); % Replace example equation with Abdulaziz's

% Then find the zero near 2:

z = fzero(f,2)

k =

4

Error using fzero (line 309)

Function value at starting guess must be finite and real.