On Sun, Nov 29, 2009 at 7:11 AM, ryan_n <rnelsonc...@gmail.com> wrote:
> Hello all,
>
> I've just started using Sage, and I'm currently trying to use the
> ode_solver class to solve some simple differential equations. I was
> having some problems setting up my own program based on this class
> until I realized that the number of points in the solution does not
> match the number of points requested by the t_span variable. For
> example, when I run this script:
> _________
> #!/usr/bin/env sage-python
> from sage.all import ode_solver
>
> def f(t, y):
> return [y[1], -y[0]]
> T = ode_solver()
> T.function=f
> T.y_0=[1, 1]
> T.ode_solve(t_span=[0, 10], num_points=100)
> print len(T.solution)
> T.ode_solve(t_span=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
> print len(T.solution)
> _________
>
> I get returned values of 101 and 10, where I would expect 100 and 11.
>
> I don't know about the first case, but for the second case, the
> solution for the last value (10) is missing. I was able to circumvent
> this problem by appending a dummy variable to the end of t_span, but
> I'm wondering if this is the expected behavior. Is there something
> about the solution that I'm missing? I am currently using Sage 4.2.1
> that I built from source in a Gentoo Linux distro.
>
Hi Ryan
The second case certainly looks like a bug
>
> In a slightly related aside, I know that y_0 are the initial
> conditions, but what if you know the conditions somewhere in the
> middle or outside your range of interest (t_span)? Would it be
> possible to input known y values as (y,t) tuples that are not
> necessarily the first values (and possibly may not get returned in the
> solution)? I've tried running the above script and getting the
> solution for a particular t value (say t=2), changing y_0 to the
> values I got for t=2, and rearrange the t_span list with 2 as the
> first value, and the results I get are not what I would expect... Is
> there something about solving these types of systems that does not
> permit using arbitrary set conditions? (I apologize if this is a
> really dumb question. I know very little about ode solving
> algorithms.)
>
>
In my case running my model to validate its behaviour, I ran it to steady
state and then used the y vector as the new y_0.
In the subsequent runm I then added an if statement to f - using your
example:
def f(t, y):
if (t == 5):
y[0] = 5
return [y[1], -y[0]]
> Thanks
>
> Ryan
>
> P.S. As this is my first post, I want to thank all of you who started/
> maintain/develop Sage. I've only been using it for a short time, but
> I'm extremely happy with what I've seen so far. I look forward to
> finding other ways to apply this tool to as many problems as possible.
>
>
It is awesome isn't it.
Anthony
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