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Re: Working on bvp4c


From: Bill Greene
Subject: Re: Working on bvp4c
Date: Mon, 22 Aug 2016 09:08:31 -0400

The last equation on page 6 in the paper shows how to evaluate f at the mid-point (f_{i - 1/2}).
It includes an _expression_ for y_{i - 1/2}. They call this a "condensed"
formulation.

On Mon, Aug 22, 2016 at 3:44 AM, lakerluke <address@hidden> wrote:
Bill Greene-3 wrote
> 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

Right, I see. So, for example, in the simple SHM ODE I pictured in my
previous post, only the derivative of y is known at the initial value, I
must therefore, as the user, provide a guess for the entire system at all
mesh values. In matlab, this is typically performed by the helper function
bvpinit.

However, in forming the global jacobian in 4.1, we need to evaluate f at mid
point mesh values, x_{i - 1/2}. Does this mean we also need to provide a
guess for the solution at these mid points? How else can we find the value
of f_{i - 1/2}?



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