optional dense output in ODE step handlers leads to weird results
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                 Key: MATH-604
                 URL: https://issues.apache.org/jira/browse/MATH-604
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 2.2
            Reporter: Luc Maisonobe
            Assignee: Luc Maisonobe
             Fix For: 3.0


The requiresDenseOutput method defined in the StepHandler interface was first 
created as an optimization feature to avoid calling computeDerivatives too many 
times for some integrators. In fact, only Dormand-Prince 8 (5,3) needs it 
because we can save 3 calls per step when the interpolator is not used.

This feature brings more problems than it solves:
* it forces users to implement this method despite its purpose is not clear,
* even if the method returns false, sometimes dense output will be generated 
(in fact when there are events detectors),
* it creates problems with at least Gragg-Bulirsch-Stoer since this integrator 
really needs interpolation,
* it will create the same problems for Adams integrators (they also need 
interpolation),
* this "optimization" is useful only for one integrator: Dormand-Prince 8 (5,3),
* in many cases, even for Dormand-Prince 8 (5,3) it does not optimize anything 
since people will often need interpolation

So I would like to completely remove this.

Removing the method is backward compatible for users.


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