Solve non-linear equation.

Hi to all,

Im solving the next equation (I use 2 different methods of writing the equation)

%Variable
syms theta
%Definicion de funciones/equaciones. 
Equation = tan(theta)- theta -0.023;
Equation_fun = @(theta) tan(theta)- theta - 0.023

To solve it I use the following methods:

%Resolucion numerica
S = fsolve(Equation_fun,0.5);
S = fzero(Equation_fun,0.5);

These methods strongly depend on the initial condition. I want to find a method that finds all the roots between 0 and 2 pi. Because of the equation I am solving. This equation represents the evolve equation. The correct answer is 0.401. It only appears when the inital condition is near the root.

Thanks for the help!

[Matt J]

How can 0.401 be the correct answer if the task is to find all roots between 0 and 2*pi?

Answer 1

[Matt J]

You can tell fzero to bound the search to a desired sub-interval.

>> fzero(Equation_fun,[0,pi/2])

ans =

    0.4012

>> fzero(Equation_fun,[3,3*pi/2])

ans =

    4.4945

It can be seen from a plot of the function that these are the only 2 roots.

     fplot(Equation_fun,[0,2*pi])