[SciPy-user] integrate.odeint , stiff chemical equations and mass conservation -any hint?
Joshua Stults
joshua.stults@gmail....
Tue Jun 2 20:31:17 CDT 2009
I think the standard way to "fix" stiff problems is to go to implicit
time-stepping.
Here's a nice write-up about using implicit time-stepping for chemical kinetics:
http://www.osti.gov/bridge/servlets/purl/45627-eDTnun/webviewable/45627.pdf
It's over a decade old, but might give you some hints on how to solve
your problem.
If you are integrating the system accurately you should be conserving
mass, even with big implicit time-steps, your production and loss
terms should balance at each step.
On Tue, Jun 2, 2009 at 4:43 PM, Anne Archibald
<peridot.faceted@gmail.com> wrote:
> 2009/6/2 ms <devicerandom@gmail.com>:
>> Hi Anne,
>>
>> Thanks for the suggestions! I didn't know about pydstool and I will
>> definitely try it.
>>
>>> On the other hand, it may be more valuable to keep the total mass as a
>>> free parameter so that you can judge the quality of your solutions by
>>> looking at how much it varies. After all, the total mass is only one
>>> direction in which your approximate solution can deviate from the true
>>> solution.
>>
>> True; however we want to use the model to predict somehow the
>> concentrations of species in a chemical system, and if mass is not
>> conserved (it goes up like 10 times) such prediction won't look good :)
>
> Indeed not, but it seems to me that there's a risk that enforcing mass
> conservation will avoid that problem but then leave you with answers
> that are just as wrong but not in an obvious way.
>
> Anne
I agree with Anne, mass conservation is a good diagnostic to help you
catch errors (modeling, coding or otherwise).
>
>>> It's also, of course, possible there's a bug in your derivative
>>> function - it's worth checking that the derivative vector is always
>>> orthogonal to the gradient of mass-as-a-function-of-your-parameters.
>>
>> Thanks for the hint, I will check it.
>>
>> m.
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--
Joshua Stults
Website: http://j-stults.blogspot.com
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