Higher Order Methods

The Euler method has an error that behaves like as . For this reason, we call it a first order method. If we have a method in which the error behaves like for some we would call it a order method.

Question: Why higher order methods?

A simple answer at this stage is that if h is small, then is even smaller, so more accuracy can be achieved with higher order methods for small h, and as h goes to zero, a higher order method will converge faster. Additional features of higher order method will become apparent later.