Re: Gray-Scott model

[Robert Munafo]

Good.

This was a great discussion. I'll try to take some of these ideas
about stability and add them to my web page describing how to compute
Gray-Scott.

I'll also make suggestions on the reaction-diffusion mailing list,
where the Ready program is discussed.

I'm not sure if you're on it, but the reaction-diffusion mailing list
is reaction-...@googlegroups.com (or
groups.google.com/group/reaction-diffusion if you want to join via the
browser)

- Robert

On 12/6/12, Federico Abella <fed...@gmail.com> wrote:
> Great! You're absolutely right about the initial conditions. Thanks a lot
> again!
> On Dec 6, 2012 2:10 AM, "Robert Munafo" <mro...@gmail.com> wrote:
>> There are two more things you might need to take care of:
>>
>> When you start the simulation, the initial pattern is usually
>> something arbitrary [...] you often need to use a
>> lower DeltaT value for the first several iterations [...]
>>
>> The stability also depends on the choice of F and k [...]

--
Robert Munafo -- mrob.com
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[Federico Abella]

Great, thanks!

By the way, for the project I had to also code different methods for solving the Gray Scott system. Runge Kutta seems to work fine, but doesn't improve much on Euler, as far as I could see. I also wrote a method which uses Runge Kutta as a first order prediction of the next time step, and then uses an implicit method to correct on it. The weird thing is, even though implicit methods are supposed to be unconditionally stable, I couldn't get a Cavalieri-Simpson method to remain stable, even using the same Deltas as in my forward Euler. Even stranger, a Crank-Nicolson method (which uses one less timestep to correct) seems to work just fine.

Have you tried any of these methods? Have you got any idea why the CS method could be more unstable?

Regards,

Federico