Re: How to use 'colloc'?

[Søren Hauberg]

On Jul 5, 2012, at 4:34 PM, c. wrote:

> 
> Il giorno 05/lug/2012, alle ore 11.56, Søren Hauberg ha scritto:
> 
>> 
>> On Jul 4, 2012, at 7:57 PM, c. wrote:
>>> for this kind of problem you could also use bim.
>>> attached is an example script to solve a particular system
>>> of 2 semilinear 2nd order ODEs with two-point boundary conditions.
>>> If you can provide more info about your specific problem I can help 
>>> you adapt the script to your needs.
>> 
>> Sounds nice! I've been using 'bvp4c' so far, which has worked out nicely, 
>> but it is kinda slow (I need to solve a system of ODE's to compute the 
>> geodesic between points on a specific manifold; as I am doing statistics on 
>> manifolds at the moment, so I usually need to compute many thousands of 
>> geodesics, so speed is kinda important). I'm looking into collocation as it 
>> seems to be rather fast (at the moment speed is more important than 
>> accuracy).
>> 
>> Is the BIM package able to give me rough solutions fast?
> Yes, I think so. Is your problem linear or non-linear?

It's non-linear :-(

> If it is a nonlinear problem the solution time depends more on the nonlinear 
> solver (in the example I used fsolve) rather than on the discretization 
> algorithm.
> But anyway the algorithm implemented in BIM (piecewise-linear Finite Elements 
> with Exponential Fitting stabilization and Mass Lumping) guarantees that the 
> Jacobian
> of the nonlinear system will have good properties that often ensure stability 
> and convergence of the nonlinear iteration.

Okay, I'll try to port my current code to the BIM package and try a couple of 
different optimizers.

Thanks
Søren