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ode and piecewise function

asked 2017-06-08 09:38:47 -0500

soking gravatar image

Hi all,

I am trying to solve, using Sage, an ode which includes a piecewise. For that I wrote the following piece of code which raises an error :

f = piecewise([(RealSet.unbounded_below_open(0),0), (RealSet.unbounded_above_closed(0),10)])
u = function('u')(x)
eqn = 2*diff(u,x) + u == f(x)
u = desolve(eqn, u, ivar=x)
show(expand(u))

Since the error vanishses when I replace the function f by either of the functions exp or log, I guess the problem is coming from the piecewise function. Could anyone help me solve this issue and explain what is wrong here?

Thanks

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Hmm, I'm not sure whether our piecewise functions are supported with Maxima's ode solvers. Note that Maxima has its own piecewise implementation which may allow this directly within Maxima.

kcrisman gravatar imagekcrisman ( 2017-06-08 09:45:30 -0500 )edit

Does it mean that I have to switch to Maxima in order to solve such ode?

soking gravatar imagesoking ( 2017-06-08 09:48:43 -0500 )edit

I don't know; I'm just suggesting that could provide a solution. Of course, for numerical solutions there are good options. Also, I believe Sage does support Dirac and Heaviside functions now so they may work fine with this and desolve.

kcrisman gravatar imagekcrisman ( 2017-06-08 12:06:46 -0500 )edit

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answered 2017-06-08 14:09:18 -0500

eric_g gravatar image

For you concrete example, you can use unit_step instead of piecewise:

sage: f(x) = 10*unit_step(x)
sage: u = function('u')(x)
sage: eqn = 2*diff(u,x) + u == f(x)
sage: u = desolve(eqn, u, ivar=x)
sage: u
(5*(e^(1/2*x) - 1)*sgn(x) + _C + 5*e^(1/2*x) - 5)*e^(-1/2*x)
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Thank you, for your answer, but could I have a more general solution because I can't apply your answer when for instance

f = piecewise([((-1,0),0), ((0,1),x), ((1,2),2-x), (RealSet.unbounded_above_closed(2),0)])

I thought of telling sage to solve the ode on each interval, but I don't see how to do it with Sage.

soking gravatar imagesoking ( 2017-06-09 03:22:51 -0500 )edit

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Asked: 2017-06-08 09:38:47 -0500

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Last updated: Jun 08