Re: bvp4c.m Question

[Jochen Broecker]

Hi Carlo,

> As I pointed out in a previous (off-list) email bvp4c is not really functional 
> yet, its
> only use at the moment can be seen as that of a starting point for someone 
> interested
> in completing its implementation.
Ok, I might have misunderstood. But thanks for clarification. The rest of 
your email was indeed helpful.

> Indeed there is a proposal to have a student to complete the implementation of 
> bvp4c
> within the GSoC 2013 program:
>
> http://wiki.octave.org/Summer_of_Code_Project_Ideas#Implement_solver_for_1D_nonlinear_boundary_value_problems
>
> If you know any interested students please encourage them to apply.
Will check.

> As things stand now, you definitely should not recommend the use of bvp4c in a 
> "production" environment.
Ok.
> If you can rewrite your problem as a 2nd order equation it is very likely that 
> you can solve it
> with a combination of the bim package and fsolve.
>
> If you want info on how to do this you should write a less abstract, yet not 
> too complicated,
> example of what you really intend to solve.
Ok. One of the problems is that I need to install octave 3.6 while 
standard distributions seem to supply only 3.2 (I know this is dummy 
stuff)

> > Questions:
> >
> > (1) My vector field has dimension 2*n, but bvp4c tries to evaluate it using
> > a 2*n-times-3 matrix. Am I supposed to return the values of the vector field
> > for each column of this 2*n-times-3 matrix? If yes, why 3? Can I tweak this
> > number? My problem allows for massive economies in terms of evaluating the
> > vector field at more than one point, but the number of points should
> > preferrably be even.
>
> I'm not really sure what you're really talking about here.
>
> The size of the matrix depends on the number of stages in
> RK methods used by bvp4c, there's not really much you can do
> about this.
>
> why do you think you need to change this? can that be done in matlab's bvp4c? 
> how?
Ok, I see now why this happens. I had the impression that matlab tries to 
evaluate my vector field at only one point at a time. But as I said, I 
don't really care about 100% compatibility with matlab. I just need to 
know how I'd have to structure my code.

> > (2) How do I provide derivatives of my boundary conditions and vector field?
> > (I want to demonstrate to people that this improves the performance.)
>
> how do you do that with matlab's bvp4c? you should be able to do the same with 
> Octave's
> implementation, if it doesn't work it's because it's not implemented yet, 
> patches are welcome.
Ok. In order to contribute (which I am happy to), I would have to look at 
the code more carefully. Please don't expect any patches in the near 
future.

In fact, I thought you SHOULD be able to provide derivatives in matlab, 
but in practice, it did not work with matlab either.

> > (3) I believe that bvp4c solves the collocation equations using fsolve. I'd
> > like to extract more information about the collocation equations at the
> > solution from fsolve (e.g. the Jacobian), but in order to interprete this
> > information, I need to know precisely how the collocation equations are
> > organised.
>
> the discretization method is an implicit 3-stage Runge-Kutta method whos 
> butcher tableau
> is given by the persistent variables A, B and C defined in the code.
>
> what the current code does is just set up the whole non linear system of 
> equations at
> all the collocation points and then let it to fsolve to solve the system.
>
> > (4) Am I right in thinking that bvp4c is a fourth order scheme, so that
> > there is an implicit assumption that (x, p) have temporal derivatives of up
> > to order 4?
>
> you can find a discussion of the convergence properties of the method in this 
> paper:
> http://dx.doi.org/10.1145/502800.502801
Good, I know that paper (more or less).

Let me think about your suggestions. And I'll cook up a simple example.

Thanks a lot,

JOchen