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?

If the problem is linear the solution time is limited only by the linear system solution, the size of the system depends

on the number of grid points you choose which is up to you.

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.

> Or do you have any thoughts on which approaches would be most suitable when speed is more important than accuracy? I can provide more details on the systems in question, but only off-line as this is still not published.

feel free to send me details off-line. I'll be glad to help if I can.

> Thanks

> Søren

c.

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