how to get minimum positive solution?

1/K (sin(u)/u-cos(u))+(2-2cos(u)-usin(u))/L=0, K,L is constant, how to get the minimum positive solution of u?

Answer 1

[Star Strider]

K = 11;  L = 13;
scu = @(u)  1/K .* (sin(u)./u-cos(u))+(2-2.*cos(u)-u.*sin(u))/L;
uv = [];
for a = 0.01:10
    us = fzero(scu, a);
    uv = [uv; us];
end
mps = min(uv(uv > 0))   % Minimum Positive Solution

[huang]

Thanks much, but how to keep K and L in the output?

[Star Strider]

My pleasure!

The K and L variables are in the same MATLAB workspace that the function and code share. As long as K and L are defined first, before the equation, and the equation is defined before the call to fzero (as I did here), MATLAB will use them appropriately in the equation.

Note that fzero has some limitations. It requires that the equation provided to it is a function of one variable only. It also only returns real results, and those only close to the initial starting point. (This is the reason I used the for loop in both answers.)