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initial conditions in desolve

asked 2011-02-21 08:56:44 -0500

Chris gravatar image

In desolve, it is possible to specify (for a second order ODE) two different types of initial conditions i.e.: y(x_0) = y_0, y(x_1) = y_1 and y(x_0) = y_0, y'(x_0) = s_0.

Is it also possible to specify initial conditions of the form y(x_0) = y_0, y'(x_1) = s_1?

Thanks!

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answered 2011-02-21 12:48:09 -0500

I believe that only Dirichlet and Neumann boundary conditions are implemented (but would happy to be proven wrong).

The relevant part of the docs is:

  • for a second-order equation, specify the initial x, y, and dy/dx, i.e. write [x_0, y(x_0), y'(x_0)]

  • for a second-order boundary solution, specify initial and final x and y boundary conditions, i.e. write [x_0, y(x_0), x_1, y(x_1)].

So the first to boundary conditions you gave are ok. But the mixed boundary conditions don't work - you'll have to get the general solution and enforce the boundary conditions semi-manually. Here's a sage notebook with examples.

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Thanks a lot, Simon! Cheers, Chris

Chris gravatar imageChris ( 2011-02-22 00:04:19 -0500 )edit

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Asked: 2011-02-21 08:56:44 -0500

Seen: 351 times

Last updated: Feb 21 '11