pushed On Mon, Feb 7, 2011 at 23:52, Barry Smith <bsmith at mcs.anl.gov> wrote:
> > On Feb 7, 2011, at 4:46 PM, Jed Brown wrote: > > > On Mon, Feb 7, 2011 at 23:35, Barry Smith <bsmith at mcs.anl.gov> wrote: > > Well what I want is why is this "the derivative we need"? There is no > hint as to an explanation why the user providing this quantity has any > meaning a all. You could just as easily say g_x where g(x) = f(x, a*x^3 + > 94) and why would that be wrong, while what you write is correct? > > > > That is the reason why I like introducing g(x) = f(x,xdot) > > > > " where xdot is approximated by the integrator as z+a*x for some a and z > depending on the integration method, step size, and past states." > > This is exactly the kind of text I want. > > > But perhaps the user (as opposed to someone implementing a new TS) > doesn't care at all and would be happy to evaluate f_x + a*f_xdot without > any knowledge of why this beast is relevant. > > The problem is not that you are providing too much information and > should take some away. The problem is you are not providing enough. Just > writing G(U) = F(t,U,U0+a*U) is not enough, you need to explain as you have > above in your sentence that the schemes DO approximate xdot in that manner > and therefor the Jacobian needed by the schemes is given by dF/dU + > a*dF/dU_t > > Barry > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-dev/attachments/20110208/62787b86/attachment.html>
