ODE System with 4 equations
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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
1 个评论
Malak Abuhusien
2021-6-14
编辑：Malak Abuhusien
2021-6-14
how solution with for loop?
采纳的回答
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.
7 个评论
Baris Gungordu
2020-5-5
Josh Meyer
2020-5-5
You can add additional inputs to the ODE function to pass in parameters, but ode45 still requires the function input to have only two inputs. So adding inputs requires that you create an anonymous function to pass to ode45:
fcn = @(t,y) ODEsystem(t,y,epsilon);
[t,y] = ode45(fcn,tspan,y0);
When fcn is created, it uses the value for "epsilon" in your workspace.
Baris Gungordu
2020-5-5
编辑：Baris Gungordu
2020-5-5
Josh Meyer
2020-5-5
This line
fcn = @(t,y) ODEsystem(t,y,eps,F_ext);
defines a function handle that calls ODEsystem with two parameters and leaves the t,y inputs available for ode45 to use. So, when you call ode45, you don't want to specify "@ODEsystem" as the function, since that function takes 4 inputs. Instead, specify the function as "fcn" which you defined with the previous line:
[t,y] = ode45(fcn,tspan,y0);
If you want to use more parameters, you can change the "ODEsystem" function to accept more inputs, and then you just need to edit the "fcn = " line to call ODEsystem with the appropriate number of extra inputs to pass in the parameter values from your workspace.
Baris Gungordu
2020-5-5
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
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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