Understand fsolve in matlab?

Hi, I have an equation along the lines of f(x,k)=sinx-kx=0, and am told to use inputs k, to return x0(k). Is someone please able to explain how I could use fsolve, or any other method to find this. I am struggling to see how to input a k using this function. Thanks

[Matt J]

So equivalently, you want to solve

    sinc(x)=k

The equation has no solution for abs(k)>=1. For abs(k)<1, it will have multiple solutions. For k=0, it will have infinite solutions. Which ones do you want?

Answer 1

[Star Strider]

I am not sure what you want to do, but this will get you started:

fn = @(x,k) sin(x) - k*x;           % Define Function  
k  = 0.5;                           % Define ‘k’ For This Solution
X0 = 2;                             % Initial Estimate For ‘x’
x = fzero(@(x) fn(x,k), X0);        % Solve for ‘x’

Note that the solution for ‘x’ depends also on ‘X0’.

Experiment with this to get the result you want.

[Hannah]

what do i then input into the command window? im presuming i cant change k in the command window at all?

[Star Strider]

You can change anything you like!

I would put this in a script instead of running it from the Command Window.

If you want to evaluate your function for a range of ‘k’ values, a loop is an option.

For example:

fn = @(x,k) sin(x) - k*x;                   % Define Function 

k = 0.1:0.1:10;                             % Define A Range For ‘k’
for k1 = 1:length(k)
    X0 = 2;                                 % Initial Estimate For ‘x’
    x(k1) = fzero(@(x) fn(x,k(k1)), X0);    % Solve for ‘x’
end

The ‘x’ vector now has a solution for each value of ‘k’.