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.
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.)
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.
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