[MATH-705] DormandPrince853 integrator leads to revisiting of state events

• Type: Bug
• Status: Closed
• Priority: Major
• Resolution: Fixed
• Affects Version/s: 3.0
• Fix Version/s: 3.0

Environment

Commons Math trunk, Java 6, Linux

• Assignee: Luc Maisonobe
• Reporter: Dennis Hendriks
• Created: 09/Nov/11 13:29
• Updated: 24/Mar/12 16:16
• Resolved: 27/Nov/11 14:34

Description

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:

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                ]

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.