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From "Dennis Hendriks (Created) (JIRA)" <j...@apache.org>
Subject [jira] [Created] (MATH-705) DormandPrince853 integrator leads to revisiting of state events
Date Wed, 09 Nov 2011 13:29:51 GMT
DormandPrince853 integrator leads to revisiting of state events
---------------------------------------------------------------

                 Key: MATH-705
                 URL: https://issues.apache.org/jira/browse/MATH-705
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 3.0
         Environment: Commons Math trunk, Java 6, Linux
            Reporter: Dennis Hendriks


See the attached ReappearingEventTest.java. It has two unit tests, which use either the DormandPrince853
or the GraggBulirschStoer integrator, on the same ODE problem. It is a problem starting at
time 6.0, with 7 variables, and 1 state event. The state event was previously detected at
time 6.0, which is why I start there now. I provide and end time of 10.0. Since I start at
the state event, I expect to integrate all the way to the end (10.0). For the GraggBulirschStoer
this is what happens (see attached ReappearingEventTest.out). For the DormandPrince853Integerator,
it detects a state event and stops integration at 6.000000000000002.

I think the problem becomes clear by looking at the output in ReappearingEventTest.out, in
particular these lines:

{noformat}
computeDerivatives: t=6.0                  y=[2.0                 , 2.0                 ,
2.0                 , 4.0                 , 2.0                 , 7.0                 , 15.0
               ]
(...)
g                 : t=6.0                  y=[1.9999999999999996  , 1.9999999999999996  ,
1.9999999999999996  , 4.0                 , 1.9999999999999996  , 7.0                 , 14.999999999999998
 ]
(...)
final result      : t=6.000000000000002    y=[2.0000000000000013  , 2.0000000000000013  ,
2.0000000000000013  , 4.000000000000002   , 2.0000000000000013  , 7.000000000000002   , 15.0
               ]
{noformat}

The initial value of the last variable in y, the one that the state event refers to, is 15.0.
However, the first time it is given to the g function, the value is 14.999999999999998. This
value is less than 15, and more importantly, it is a value from the past (as all functions
are increasing), *before* the state event. This makes that the state event re-appears immediately,
and integration stops at 6.000000000000002 because of the detected state event.

I find it puzzling that for the DormandPrince853Integerator the y array that is given to the
first evaluation of the g function, has different values than the y array that is the input
to the problem. For GraggBulirschStoer is can be seen that the y arrays have identical values.

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