Divergent solution using ode45
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I have a code (see below) that solve the second order differential equation. As a output it gives the position and velocity as a function of time. For some values of omega 0.48,0.5,0.85 it gives the diverging solution of position. I guess this is due to some error but I can not find the error. How to overcome this errors for above omegas. Please help regarding this. I am new to MATLAB.
%% MAIN PROGRAM %%
t=linspace(0,1000,5000);
y0=[1 0];
omega=0.85;
[tsol, ysol]=ode45(@(t,y0) firstodefun4(t,y0,omega), t, y0, omega);
position=ysol(:,1);
velocity=ysol(:,2);
%% FUNCTION DEFINITION%%
function dy=firstodefun4(t,y0,omega)
F=1;gamma=0.01;omega0=1;
kappa=0.15;
dy=zeros(2,1);
dy(1)=y0(2);
dy(2)=2*F*sin(omega*t)-2*gamma*y0(2)-omega0^2*(1+4*kappa*sin(2*omega*t))*y0(1);
end
0 Comments
Answers (2)
Torsten
on 9 Sep 2022
Edited: Torsten
on 9 Sep 2022
We don't know the reason - technically, your code is correct. Although I would change it as shown below.
What makes you think that the solution you get is incorrect ? Do you have any indication that it should be bounded as t -> 00 ? For me, the behaviour looks very regular.
%% MAIN PROGRAM %%
t=linspace(0,50,5000);
y0=[1 0];
omega=0.85;
F=1;
gamma=0.01;
omega0=1;
kappa=0.15;
[tsol, ysol]=ode45(@(t,y0) firstodefun4(t,y0,omega,F,gamma,omega0,kappa), t, y0);
position=ysol(:,1);
velocity=ysol(:,2);
plot(tsol,position)
%% FUNCTION DEFINITION%%
function dy=firstodefun4(t,y0,omega,F,gamma,omega0,kappa)
dy=zeros(2,1);
dy(1)=y0(2);
dy(2)=2*F*sin(omega*t)-2*gamma*y0(2)-omega0^2*(1+4*kappa*sin(2*omega*t))*y0(1);
end
4 Comments
Jano
on 14 Oct 2022
Is it possible for this to accept a range of value for omega, for example omega = [0.85:5].
Sam Chak
on 12 Sep 2022
Hi @Abhik Saha
If you reduce the value for , then the system should be stable.
% MAIN PROGRAM %
n = 400;
t = linspace(0, n*100, n*10000+1);
y0 = [1 0];
omega = 0.85;
F = 1;
gamma = 0.01;
omega0 = 1;
kappa = 0.1469;
[tsol, ysol] = ode45(@(t, y) firstodefun4(t, y, omega, F, gamma, omega0, kappa), t, y0);
position = ysol(:, 1);
velocity = ysol(:, 2);
plot(tsol, position)
% ODE
function dy = firstodefun4(t, y, omega, F, gamma, omega0, kappa)
dy = zeros(2,1);
dy(1) = y(2);
dy(2) = 2*F*sin(omega*t) - 2*gamma*y(2) - omega0^2*(1 + 4*kappa*sin(2*omega*t))*y(1);
end
3 Comments
Sam Chak
on 13 Sep 2022
@Abhik Saha, I changed the value of κ (via trial-and-error) because I thought of reducing the effect of the periodic function in the term. The original should be restored. You can definitely run the simulations for different values of angular frequency ω. There is nothing wrong about the response being divergent as (unstable).
You need to work out the algebra in order to find out fundamental matrix solution of the system, so that you can determine the stability codition following from the Floquet theorem. You can watch some videos here:
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