Numerical representation

[Jon Herman]

Sorry Robert, I'd missed your post when I just made my last one. The output
I am getting in Python looks as follows:

array([  9.91565050e-01,   1.55680112e-05,  -1.53258602e-05,
        -5.75847623e-05,  -9.64290960e-03,  -8.26333458e-08])

This is the final state vector, consisting of 6 states (postion and
velocity), although this isn't really relevant right now.

In MATLAB, using the same process for the RKF78, I get the following output:

Xend =

  Columns 1 through 3

    9.915755153307796e-001    3.592556838089922e-016
-1.523933534321440e-005

  Columns 4 through 6

   -7.175069559491303e-015   -9.624755221500220e-003
1.289789641929434e-017

As you can see, the results are close but there is a big difference in
precision (the 2nd, 4th and 6th entries are supposed to be zero under the
intial and final conditions I am running).
See also the post I just made where you can see the Python code I am using
(MATLAB code is identical but translated)

This is for a fixed timestep in both Python and Matlab. If I let the code
run with an identical method for timestep correction (based on a tolerance),
Python will use a timestep approximately 10^5 SMALLER than Matlab uses. So
I'm really sure it's not a representation issue, but actually a precision
issue.

Thanks for any advice!
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