forward euler for a system of equations

Hello,

I am trying to implement a code for a system of three equations and I am trying to use the for loop. importantly I want to plot the three function in the same graph , but I get a weird behaviour !

the time step is dt=0.02(suppose) my functions are phi, ro and om

t1=500;

t0=0;

t(1)=t0;

phi(1)=pi/6;

ro(1)=0;

om(1)=1;

for j=1:t1:dt

t(j+1)=t0+j*dt;

phi(j+1)=(dt*ro(j))+(phi(j));

ro(j+1)=(ro(j)*(1-dt*0.2))(19.6*dt*sin(phi(j)))+(16*(om(j)^2)*sin(phi(j))*cos(phi(j))*dt);

om(j+1)=(om(j))+(dt*0.05*cos(phi(j)))-(0.0125*dt);

end

plot(t,phi,"b--")

hold on

plot (t,ro,"r")

hold on

plot (t,om,"y")

Can you please spot where I slipped up ? in forward euler for a small dt functions should nomaly converge ! but i am getting a constant function om and other are keep on changing !

[John D'Errico]

But you need to tell people what the equations really should be! Otherwise, we don't know what you did wrong, without extensive guesswork on our part.

Answer 1

[James Tursa]

I'm assuming this

for j=1:t1:dt

was meant to be something like this

for j=1:t1/dt

[Karl Campos]

it is the time loop so it is from 1 to t1 with a time-step of dt , so I don't think what you wrote mr james

[James Tursa]

No. j is an index loop that is used to calculate time via this equation

t(j+1)=t0+j*dt;

j is not, in and of itself, a time loop that goes from 1 to t1 with a time-step of dt. If you were to step j at a rate of dt like you suggest and then use it as an index you would get an error. Thus, I still think you need this:

for j=1:t1/dt