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https://issues.apache.org/jira/browse/MATH-380?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13114278#comment-13114278
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Luc Maisonobe commented on MATH-380:
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A first attempt to implement Jacobians computation again in ODE has been 
committed in subversion repository as of r1175409.
This implementation still lacks the ability for step handlers to also retrieve 
the additional equations and their derivatives.
This implementation is based on the Orekit one described here: 
[https://www.orekit.org/blog/public/vpommier-ISSFD-2011-extended_propagation.pdf]

> Need to (re)initialize dYdY0 for multiple integrate with 
> FirstOrderIntegratorWithJacobians
> ------------------------------------------------------------------------------------------
>
>                 Key: MATH-380
>                 URL: https://issues.apache.org/jira/browse/MATH-380
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 2.1
>            Reporter: Pascal Parraud
>            Assignee: Luc Maisonobe
>            Priority: Minor
>             Fix For: 3.0
>
>
> There is a lack in the method integrate of FirstOrderIntegratorWithJacobians. 
> The jacobian DYDY0 can't be initialized by the user, unlike DFDP with DF0DP.
> So, for several successive integrations, the matrix is reinitialized to 
> identity and that is not what we might want.

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