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Python function in ODE not producing needed results

asked 2015-10-29 10:22:05 -0500

calc314 gravatar image

I am using the dirac_delta function in an ODE, and since it is treated like a Python function, it is not evaluated as I would like in the ODE solver. I think this is a matter of having a Python function when I need a symbolic function, but I cannot figure out how to get around it. My code is below. Any ideas?

var('A p y t s v')
A=3
p=2
alpha = 1
beta = -1/sqrt(3)
omega = 1
F(t) = [SR(1),v,-omega^2*y+A*dirac_delta(t-p)]
ans=desolve_odeint(F(t),[0,alpha,beta],srange(0,5,0.1),[s,y,v],ivar=t)
ty=[[a[0],a[1]] for a in ans]
tv=[[a[0],a[2]] for a in ans]
line(ty)+line(tv,color='red')
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Comments

I think you are right. It's possible that Maxima would have an implementation of Dirac delta that you could use directly within Maxima, though.

kcrisman gravatar imagekcrisman ( 2015-10-29 14:31:20 -0500 )edit

Is there a way to use the ode solver with a python function in the vector field? I think I've done this before but what I tried in the past does not seem to work.

calc314 gravatar imagecalc314 ( 2015-10-29 15:28:53 -0500 )edit

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answered 2015-10-29 20:45:33 -0500

calc314 gravatar image

In the end, I used ode_solver and an approximation of the delta function to get things working. Here is the code:

@interact(layout=[['A','p','interval'],['alpha','beta','omega']])
def lab(A=input_box(2,label='A',width=15),p=input_box(2,label='p',width=15),alpha = input_box(1,label='alpha',width=15),beta = input_box(1/sqrt(3),label='beta',width=15),omega = input_box(1,label='omega',width=15),interval=input_box((0,6),label='interval',width=20) ):
    def f(q):
        w=0.001
        if q>p-w/2 and q<p+w/2:
            return(1/w)
        else:
            return 0

    def dy(t,y):
        return [ 1, y[2], -omega^2*y[1]+A*f(y[0]) ]

    T=ode_solver()
    T.function=dy
    T.ode_solve(y_0=[0,alpha,beta],t_span=interval,num_points=500)
    ans=T.solution
    ans=[a[1] for a in ans]
    ty=[[a[0],a[1]] for a in ans]
    tv=[[a[0],a[2]] for a in ans]
    p=line(ty,legend_label='y (position)')+line(tv,color='red',legend_label='v (velocity)')
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Asked: 2015-10-29 10:22:05 -0500

Seen: 42 times

Last updated: Oct 29 '15