ODE solver-using initial conditions in events function
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I want to solve a second-order ODE (time derivatives on x) using numerical solver like ode45:
mx''+cx'+kx+F1=0
where F1 is a nonlinear function of x and it's initial value x(0). But when x becomes x(0)-5, I want F1 to stop functioning and switch the ODE to
mx''+cx'+kx+F2=0
where F2 is just a constant and I will simulate it until x' is zero.
I know how to set event functions to make the integration stop at x'=0, but how can I switch between F1 and F2? Event functions seem not to support using initial conditions in the event describing.
One background is that F1 and F2 can be merged. When x becomes x(0)-5 and further, F1 will be a complex number while it's real part is just F2, so I can solve one equation
mx''+cx'+kx+real(F1)=0
until x' is zero. But then the simulation will not give a fine resolution at the switching point of F1 and F2. So if anyone can suggest a way to make fine resolution near the switching point of F1 and F2, that also solves my issue. Thank you!
采纳的回答
If you want to use the event option, you can pass x(0) as an additional argument to the event function function and return control to the calling program when x(0)-5 is reached.
I suggest you just use mx''+cx'+kx+real(F1)=0 and choose tspan fine enough to resolve the switching point.
3 个评论
Haocheng Yang
2022-3-1
Yes I understand the second way, thought it will lower the overall simulation speed as I don't need very fine steps outside the switching point.
I also tried to include x(0) in the event function but not successful. I converted that second order equations to two first order equations, so I define two initial conditions
x_initial=[x0 v0] and options=odeset('Events',@onedof_events)
The part running the solver is
[tout,xout]=ode45(EOM,[t0 T],x_initial,options)
and my event function is
function [value isterminal direction]=onedof_events(t,x,x_initial)
value=x_initial(1)-5-x(1);
isterminal=1;
direction=0;
end
But this gives me error like "Not enough input arguments." and the full messages are here
Would you have any suggestions on this issue?
Torsten
2022-3-1
options=odeset('Events',@(t,x)onedof_events(t,x,x_initial)
instead of
options=odeset('Events',@onedof_events)
But you don't need to care how long the tspan vector is - the steps the solver takes are independent from how many elements tspan comprises.
Haocheng Yang
2022-3-2
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