> > Hi:

> >  Given dy/dt = a*y+f, and we want to estimate the value of a by
> > measuring

> > the value of y for a given f. The question is how many different f
> > should

> > we set as the input so that we have enough output(s) of y to estimate
> > a?

> If y(0) = y0, the solution of the DE is y(t) = -(f/a) + (f+y0*a)*exp
> (a*t)/a, so if you know y0 it is enough to measure y at one non-zero
> value of t. If you don't know y0, you need two measurements, y1 = y
> (t1) and y2 = y(t2). This gives two nonlinear equations to be solved
> for y0 and a. These can be tackled numerically using your favorite
> equation-solving routine.

> R.G. Vickson

> >  Suppose we are dealing with a PDE like pdiff(u, t, 1) = a*pdiff(u, x,
> > 2)+f

> > where pdiff(u, x, 2) means twice partial derivate of u to x. Again we
> > want

> > to estimate a for given f and measuremnt u. What are the extra

> > considerations we have, compared with the case when we deal with

> > only ode?

> >  Thanks,- Hide quoted text -

> - Show quoted text -