Re: Working on bvp4c

[lakerluke]

Thanks for the pointer! That really helps. So don't worry about answering my
questions from the previous post. In light of your comment I think I
understand the approach intended by the Shampine paper. We use Newton's
method to look for roots for the system (4.1) which gives us our solution at
mesh points. As pointed out in the paper in order to apply this method we
must compute the jacobian of the terms in the system (4.1). This in turn
requires us to compute the partial derivatives of the f and g functions. I
think the paper then goes on to explain that in order to form these partial
derivative terms we consider the Jacobians of f (I will refer to these
Jacobians as [1]):

J_{i} = (partial f_{i}) / (partial y)

J_{i - 1/2} = (partial f_{i - 1/2}) / (partial y)

We then compute these using finite difference to then use in the global
Jacobian (printed in the middle of page 7):

(partial phi_{i}) / (partial y_{i})

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?

Luke



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