solving systems of nonlinear equations in matlab

In MATLAB, solving systems of nonlinear equations can be done using numerical methods such as Newton-Raphson method, Secant method, and Broyden's method. Here's an example of how to solve it using the Newton-Raphson method:

Suppose we have a system of nonlinear equations:

main.m
f1(x, y) = 2x^2 + 3y^2 - 8x - 12y + 8 = 0
f2(x, y) = x^2 - y^2 + 4x - 4y + 3 = 0
81 chars
3 lines

We want to find the values of x and y that satisfy both equations. We can define a function that returns the values of the equations:

main.m
function [f1, f2] = system_equations(x, y)
f1 = 2*x^2 + 3*y^2 - 8*x - 12*y + 8;
f2 = x^2 - y^2 + 4*x - 4*y + 3;
end
116 chars
5 lines

Then, we can use the fsolve function in MATLAB to solve the system of equations numerically using the Newton-Raphson method:

main.m
options = optimoptions('fsolve','Display','iter');
[x, fval, exitflag] = fsolve(@system_equations, [0, 0], options);
117 chars
3 lines

Here, options is an option set used to display information about the algorithm iterations. fsolve returns the values of x, the values of the function f at x, and the exit flag of the algorithm. The initial guess for x is 0.

The solution of the system of nonlinear equations is given by x = [1.5, 1] (with some variation due to the numerical method).

Note that fsolve can also be used to solve a system of equations with more than two variables by defining a function that returns the values of all equations.