[jira] [Commented] (MATH-172) implementation of implicit Runge-Kutta method for stiff differential equations

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[jira] [Commented] (MATH-172) implementation of implicit Runge-Kutta method for stiff differential equations

Gilles (Jira)

    [ https://issues.apache.org/jira/browse/MATH-172?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13093995#comment-13093995 ]

Luc Maisonobe commented on MATH-172:
------------------------------------

Yes, there have been some work on it. Nothing has been committed yet.
The work was based on the patch attached to this issue, which is an implementation of BDF (Backward Differential Formula). There are some stability problems with Adams methods and the BDF formula shares (or could share) some code with Adams.
I first thought simply computing the new point by applying the formulas from high order to low order (i.e. from small to large numbers) would be sufficient to solve these numerical instabilities. I was wrong. Another attempt could be made now that we have MathUtils.linearCombination, which can compute accurate linear combinations even when cancellations occurs, which by construction do happen in these algorithms.

I would really much like to have stiff ODE solver in 3.0.

If you want to help solving this issue, do not hesitate to propose something.

> implementation of implicit Runge-Kutta method for stiff differential equations
> ------------------------------------------------------------------------------
>
>                 Key: MATH-172
>                 URL: https://issues.apache.org/jira/browse/MATH-172
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 1.2
>            Reporter: James Housden
>            Assignee: Luc Maisonobe
>             Fix For: 3.0
>
>         Attachments: bdf-2009-07-07.patch
>
>
> In version 1.2 several explicit Runge-Kutta methods have been implemented which work fine for non-stiff problems. However these methods are not suitable for stiff equations. The implementation of an implicit Runge-Kutta method such as Radau5 would extend the functionality of the ode package to cover the solution of stiff ordinary differential equations.

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