Re: Working on bvp4c

[Bill Greene]

As a proof-of-concept, I did a quick and dirty C++ implementation of bvp4c.

One of the main purposes was to test the Sundials/Kinsol nonlinear algebraic

solver for this application. In that regard, I would say my experience has been

mixed. My impression is that, even with line search enabled, it is not as effective

at coping with poor initial guesses as MATLAB bvp4c.

This implementation computes a dense jacobian by finite difference (FD). I had hoped to

try FD computation of a sparse jacobian but have not done that yet. But even this

dense jacobian code has better performance than I expected.

The main limitation (that I know of) of my little test code is that it doesn't compute

 discretization errors and refine the mesh; it simply computes a solution with the

input mesh.

If you have any interest in looking at the code, it is here:

https://github.com/wgreene310/bvp1d

Bill Greene 

On Fri, Aug 12, 2016 at 6:56 PM, c. <address@hidden> wrote:

On 6 Aug 2016, at 15:38, lakerluke <address@hidden> wrote:

> Now in order to form the Jacobian terms [1] the paper says they use the
> function numjac to calculate the partial derivatives. I believe Octave does
> not have such a function...
>
> Does anyone know of any equivalent method in octave to numjac? Do you think
> this is something I am going to have to implement first?

There are functions to compute numerical jacobians in the optim package,
I believe the code of one such functions is replicated in ode23s in the
package odepkg to avoid placing a dependency of odepkg on optim.

I highly recommend having an m-file only implementation of bvp4c, at
least as a first step.

c.