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Euler's method in matlab

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Haya Ali
Haya Ali on 2 Sep 2021
Edited: Haya Ali on 8 Sep 2021
If I write the model using Euler's method. Like this
clear all; close all; clc;
%value of constants
a_n=0.1;
omega_0=2;
dt=0.01; %step size
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x(1)=1;
y(1)=1;
for i=2:1000
x(i)=x(i-1)+((a-x(i-1)^2-y(i-1)^2)*x(i-1)-omega_0*y(i-1))*dt;
y(i)=y(i-1)+((a-x(i-1)^2-y(i-1)^2)*y(i-1)+omega_0*x(i-1))*dt;
end
Does that mean it will give me values of x and y instead of dx/dt and dy/dt?

Accepted Answer

Fabio Freschi
Fabio Freschi on 2 Sep 2021
Edited: Fabio Freschi on 2 Sep 2021
Any ODE solver gives the unknown function(s) as result, not its derivative. So, yes, your results are x and y.
Note that in your solution you forgot the term

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