how to use fsolve in matlab

fsolve is a built-in function in MATLAB to solve nonlinear equations or systems of equations. Here is the syntax to use fsolve:

main.m
[x,fval,exitflag,output] = fsolve(fun,x0,options)
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where:

• fun is the function to solve. It can be an anonymous function or a function handle.
• x0 is the initial guess.
• options is an optional structure to set the algorithm parameters.

The output x is the solution to the equation, fval is the value of the function at x, exitflag is the reason for termination and output is a structure containing information about the optimization process.

Here's an example code to solve the nonlinear equation x^2 = sin(x) using fsolve:

main.m
fun = @(x) x^2 - sin(x); % define the function
x0 = 1; % set the initial guess
options = optimoptions('fsolve','Display','iter'); % set the options
[x,fval,exitflag,output] = fsolve(fun,x0,options); % solve the equation
disp(x); % display the solution
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This code sets the initial guess to 1, sets the display option to 'iter' to display the progress of the optimization process, and then calls fsolve to solve the equation. Finally, it displays the solution.

Note that fsolve can be used to solve systems of equations as well. In that case, fun should be a vector function that returns the values of all the equations at the given point.