[petsc-dev] manual page for TSSetIJacobian()

[Barry Smith]

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