[petsc-dev] manual page for TSSetIJacobian()

[Jed Brown]

On Mon, Feb 7, 2011 at 22:19, Barry Smith <bsmith at mcs.anl.gov> wrote:

> It uses U0 but never explains what it is. It also calls a the "shift" but
> never explains what it is. Perhaps some notes explaining this stuff would
> make the solver more transparent. And a reference to further material that
> uses this approach would be great if it exists.


Suppose we have f(x,y). There are two ways to express the derivative we need

1. f_x(x,y) + a*f_y(x,y)
2. g_x where g(x) = f(x,z+a*x)

I used version 2 in the man page because I think 1 looks arbitrary and is
less obvious how it arises from a time integrator. There is a note later in
the page about the equivalence. I suppose the name "shift" is more natural
for version 1. Do you think I should make version 1 primary (or remove any
mention of 2)?

Do you have a better name for "shift", or just want more text (I felt like
elaborating would be describing a simple equation in words)?
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