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Re: [Help-gsl] ODE solvers and overdamped motion


From: Jonny Taylor
Subject: Re: [Help-gsl] ODE solvers and overdamped motion
Date: Fri, 11 Sep 2009 12:04:55 +0100

Thanks very much for your reply. I had a brief try with the implicit solvers, but didn't have a huge amount of luck. What I found was: 1. They do manage to approach closER to zero, but still do show some unstability, albeit on a lower level 2. While the timesteps are slightly larger it seems that, in this simple case at least, the number of samples required is around three times as large (and fairly independent of error tolerance when the system is close to zero). 3. The implicit methods sometimes request derivatives to be evaluated at massively outlying points (e.g. 1e6).

(1) is an improvement, but a monotonic decrease in abs(y) would have been nice. (2) is a big disappointment because my highest priority is lower run-time. (3) causes quite a few problems because evaluating such configurations accurately is difficult to impossible, and I am wary about "lying" to the solver in my response without knowing what knock-on effect that might have.

Does this sound like what you would expect, or am I still misusing something?

Cheers
Jonny

On 11 Sep 2009, at 11:26, Frank Reininghaus wrote:

Hi,

2009/9/11 Jonny Taylor <address@hidden>:
the issue I am having can be seen in a simple overdamped spring
calculation (the derivatives function simply returns dydt[i] = -y [i] * 9.0).

Such ODEs are called 'stiff equations', see

http://en.wikipedia.org/wiki/Stiff_equation

This makes me wonder
if there is something I can do, or a different stepper I can use, that will improve the performance. I wonder if fundamentally the problem is that the
motion involved is exponential decay

This is indeed the case. You might want to try one of the implicit ODE solvers.

Best regards,
Frank





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