# ODE System with 4 equations

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Baris Gungordu 2020 年 5 月 5 日

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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Malak Abuhusien 2021 年 6 月 14 日
how solution with for loop?

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### 採用された回答

Josh Meyer 2020 年 5 月 5 日

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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Baris Gungordu 2020 年 5 月 5 日
Great, many thanks.

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