fsolve in matlab

To solve equations numerically in MATLAB, you can use the fsolve function. fsolve is a built-in function in MATLAB that helps you to find the roots (or zeros) of a system of nonlinear equations.

Here is an example of how to use the fsolve function:

main.m
% Define the equation(s) you want to solve
fun = @(x) x^2 - 2;

% Initial guess
x0 = 1;

% Call the fsolve function
x = fsolve(fun, x0);

% Display the result
disp(['The solution is x = ', num2str(x)]);
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In this example, we want to solve the equation x^2 - 2 = 0. The fun variable is defined as an anonymous function that represents the equation. The x0 variable is the initial guess for the solution. The fsolve function is then called with fun and x0 as inputs, and it returns the root of the equation. Finally, the result is displayed using the disp function.

You can use fsolve to solve systems of nonlinear equations as well by defining a vector-valued function. For example:

main.m
% Define the equations you want to solve
fun = @(x) [x(1)^2 + x(2) - 4; x(1) + x(2)^2 - 7];

% Initial guess
x0 = [1; 1];

% Call the fsolve function
x = fsolve(fun, x0);

% Display the result
disp(['The solution is x = [', num2str(x(1)), ', ', num2str(x(2)), ']']);
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In this example, we want to solve the system of equations x^2 + y - 4 = 0 and x + y^2 - 7 = 0. The fun variable is defined as a function that returns a vector [f1; f2] where f1 and f2 correspond to the two equations. The x0 variable is the initial guess for the solution, given as a vector. The fsolve function is called with fun and x0 as inputs, and it returns the root of the system of equations. The result is then displayed.