On Mon, Feb 7, 2011 at 23:35, Barry Smith <bsmith@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. 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.