where is the cell in the abcsisa and is the first abcisa. M is a bound for the second derivative of the ODE unknown and is the Lipschitz continuity property bound. This is derived in most of numerical analysis books.
My question is the following: Having small is good for convergence and stability (right?) in the sense that small implies little change. If then the function (on the right hand side of the ODE) is constant on y. If the function is contracting. So why is in the denominator of the bound? My intuition (which is not working good) says that the error bound should diminish as diminshes.
What is wrong with my intuition here?