Re: Working on bvp4c

[c.]

On 12 Jul 2016, at 12:59, lakerluke <address@hidden> wrote:

> Thank you for the response and the resource, Carlo. I am now looking through
> that pdf and analysing the code in bvp4c.m to look at ways of improving the
> script. If anyone else has any resources they think would be useful for this
> project, please let me know.

Hi Luke,

Thanks again for your interest in contributing to
bvp4c for Octave.

Others on this list have expressed their 
interest in improving this function,
so if anyone has done anything in that 
direction I hope he/she jumps into
this discussion to discuss the current status
and avoid duplication of effort.


As for my initial implementation, as I already
said it is extremely crude and I don't think
it reflects the correct algorithm described in 
the Shampine paper [1].

All it does at the moment is set up the residual 
for a nonlinear problem using Simpson's rule and
let fsolve do the rest.

The error estimate for mesh refinement is even more
naive as it just compares y' computed with first order 
finite differences to the evaluation of f(t,y) at interval 
midpoints instead of applying the integral-norm-based 
approach of [1].

HTH,
c.

[1] Kierzenka, Jacek, and Lawrence F. Shampine. 
"A BVP solver based on residual control and the Maltab PSE." 
ACM Transactions on Mathematical Software (TOMS) 27.3 (2001): 299-316.