Are error formulas for numerical methods appliable for any step size, or can they only be applied when the method converges?
The example that motivated this question was the following formula for the error of Heun's method (Runge-Kutta order 2).
$E = (\frac{1}{4}||f_y||_{\infty} ||y^{(2)}||_{\infty} - \frac{1}{12}||y^{(3)}||_{\infty})h^3$
This formula grossly underestimates the error when the step size is big. (Note, however, that I do not know if this formula is correct)