- What is ‘fsolve’ in MATLAB?
- What is a System of Non-linear Equations?
- How to Solve Non-linear Equations in MATLAB Using fsolve Command
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?
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.
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:
x = 0:pi/100:2*pi;
y = sin(x);
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 – x2 – 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))];
- 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);
- 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:
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.
Abdul Mannan is an Electrical Power Engineer with specialization in High Voltage. He’s the founder and former president at Youth Entrepreneurship Society (YES), University of Engineering & Technology Taxila Campus. He is the leading contributor at “Right to Write”. Connect with him about Entrepreneurship, startup ideas, creative writing, business strategies via linked in.