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

["Luc Maisonobe (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/MATH-172?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Luc Maisonobe updated MATH-172:
-------------------------------

    Attachment: bdf-2009-07-07.patch

Progress has been slow on this issue but lots of works has been already done. A new integrators hierarchy for multi-step integrators has been developed and committed into the subversion repository for 2.0. This hierarchy however is complete only for Adams-Bashforth and Adams-Moulton methods (which have been enhanced to adaptive step size). Both methods are in the non-stiff category, but Adams-Moulton can sometimes be tried on stiff problems, it may work there ...

For real stiff problems, though, a better method is needed. One well-known method is BDF (Backward Differential Formulas) which comes from Gear's work. An attempt to implement this (still with adaptive step size thanks to Nordsieck representation) has been done. This patch contains the current step of this attempt. It does *not* work yet! The error estimation leads either to too small steps or too large number of evaluations. Although the current state does not prevent user from using methods with order larger than 6, despite these methods are known to be unstable. This will be fixed in the final tuning of the code.

This patch is attached here because this issue has been blocking the release of 2.0 for too long now, so it was decided to postpone it after 2.0. In the meantime, this patch could be helpful for people wanting to have a clue about this issue. One possible way is to remove the adaptive step size stuff (but beware of event handling which is much simpler when steps truncation is possible). Work will continue on this issue after 2.0 has been released, based on this patch.

Sorry for the delay and very partial fix we were able to provide at this time.

> 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: 2.0
>
>         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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