**What is ‘fsolve’ in MATLAB?****What is a System of Non-linear Equations?****How to Solve Non-linear Equations in MATLAB Using fsolve Command****Conclusion****References**

## What is ‘fsolve’ in MATLAB?

‘fsolve’ is a built-in function in MATLAB to solve nxn system of non-linear equation without showing iterations. Function to be solved must be a continuous function and ‘fsolve’ only gives one root.

## What is a System of Non-linear Equations?

### Definition

A system of ‘n’ (n>0) number of equations having ‘n’ number of variables in which at least one equation is not linear i.e. Its solution must not plot a linear graph. In other words, standard form of linear equation is:

C1x + C2y + C3 = 0

Any equation that cannot be written in this form will be a non-linear equation.

### Description

Let’s suppose:

y=f(x) % ‘y’ is a function of ’x’.

In non-linear equation, ‘x’ is not directly proportional to ‘y’ and the graph is not linear. It can be a parabola, circle, hyperbola, curve etc.

Take an example:

*MATLAB
Code: *

x = 0:pi/100:2*pi;

y = sin(x);

plot(y)

A sine wave can be seen in fig.1 which is not linear.

## How to Solve Non-linear Equations in MATLAB using ‘*fsolve*’ Command?

We can solve nxn non linear system in MATLAB using a built-in command “fsolve” without showing iterations.

### Steps to Solve Non-linear Equations in MATLAB

Following are the steps to solve any non-linear equation using ‘fsolve’ command in MATLAB:

- Take an example:

*F(x,y)
= 2x – y – e ^{-x }*

*G(x,y)
= 2y – x ^{2} – e^{-y}*

- Make a function of the equation in editor of MATLAB and save it in the known location.

function F = ftn_fsolve_example(X)

x = X(1);

y = X(2);

f = 2*x-y-exp(-x);

g = 2*x-x.^2-exp(-y);

F = [f;g];

% Alternatively, you could do the following. It’s more compact , but harder

% to read;

% F = [2*X(1) – X(2) – exp(-X(1)); -X(1).^2 + 2*X(2))];

End

- Write a code calling the ‘fsolve’ function in the new script.

% script fsolve example

a = @ftn_fsolve_example;

X0 = [1;1]; % initial guess

X = fsolve(a,X0);

disp(X);

- Output will be shown as:

- If we do not want the output in descriptive form, we can introduce a third variable in MATLAB code named “options”.

options = optimset(‘display’,’off’);

- Now the output will show like this:

## Conclusion

The ‘fsolve’ command in MATLAB is quite useful in solving the roots of non-linear equations without iterations. The function to be solved must be a continuous function and ‘fsolve’ only gives one root.