ODE System with 4 equations

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Baris Gungordu
Baris Gungordu 2020-5-5
评论： Torsten 2022-9-25
Hi all,
I have a system with 4 ODEs which I want to solve simultanously.Each equations are feeded with some variables. All derivatives are with respect to time (t) only. The variables are x,v,p and u.
dx/dt = v(t)
dv/dt = - 2*v(t) - 1000*x(t) - p(t)
dp/dt = v(t) - u(t)
du/dt = p(t) - abs(u(t) * u(t)
Initial conditions are all zero at t = 0, i.e. x(0) = 0; v(0) = 0; p(0) = 0; u(0) = 0.
Looking forward to get your help.
I don't have any preference over the integration scheme but an application of ode45 should help. I also have access to the symbolic toolbox.
Best regards,
Baris

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Josh Meyer
Josh Meyer 2020-5-5
编辑：Josh Meyer 2020-5-5
When you have a system of equations, each equation gets its own spot in the solution vector y.
With the conventions
y(1) = x, dydt(1) = dx/dt
y(2) = v, dydt(2) = dv/dt
y(3) = p, dydt(3) = dp/dt
y(4) = u, dydt(4) = du/dt
You can write the system of equations in an ODE function as
function dydt = ODEsystem(t,y)
dydt = zeros(4,1);
dydt(1) = y(2);
dydt(2) = - 2*y(2) - 1000*y(1) - y(3);
dydt(3) = y(2) - y(4);
dydt(4) = y(3) - abs(y(4) * y(4));
end
After you save the function in a file in your current directory, you can set the initial conditions and integrate with:
y0 = zeros(4,1);
tspan = [0 10];
[t,y] = ode45(@ODEsystem,tspan,y0);
plot(t,y,'-o')
For your problem, with the initial conditions all zero, this integration doesn't do much because all of the terms in the equations depend on x, v, y, or p, so the terms all remain zero.
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RITIKA Jaiswal
RITIKA Jaiswal 2022-9-25
what do do if we have odes of dimension 100.Since it was of order 4 we can easily write that but what if have order of 100 how can we implement that in our code?
please help.
Torsten
Torsten 2022-9-25
If there are regularities in the dydt terms, you can usually use a loop to set them up.
If not, you will have to write them down one by one.

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