Re: Working on bvp4c

[Bill Greene]

Glad the code was useful, Luke.

Not sure I understand your question, though. Yes, equation 4.1 is the key to

the algorithm and, yes, it needs to be solved for Y by some Newton-like

method. 

The user is required to provide the initial values for *all* the

components in Y as solinit.y. That initial guess and the function defining

Phi is all the KINSOL solver needs to find the Y that satisfies 4.1.

Bill

On Sat, Aug 20, 2016 at 12:43 PM, lakerluke <address@hidden> wrote:

Thanks Bill, that is very useful.

I have another silly question to ask. I'm failing to understand a
fundamental element related to implementing bvp4c from the Shampine paper.

We form the system [4.1] (pg. 6) by applying the Simpson method to the
original system. We then proceed to solve this by use of Newton's method to
find the roots of the system [4.1]. This leads to an iterative method where
we use the value of the solution at the boundary to form an approximation to
the solution at the next value of the mesh.

I have written this up on some paper to hopefully better explain my
question. If someone could correct my understanding, that would be much
appreciated.

<http://octave.1599824.n4.nabble.com/file/n4679349/bvp4c_issue1.jpg>

Best regards,

Luke



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