Adams-Bashforth initial points influence in error

Question

I want to know how important is the method used for computing the first 3 steps of an Adams-Bansforth explicit method of fourth order. Is there a substantial difference if I compute the initial steps with a method of first order like euler's method and not for example with a method of fourth order like Runge-Kutta?

Answer 1

The error of the first steps gets propagated to contribute to the global error. If you start with steps with local error $O(h^2)$, then the global error will also be dominated by this error order.

When using RK4 for the first steps, the local error is $O(h^5)$ which then gets dominated by the accumulation of the other local errors of the AB4 steps.

See Deriving the central Euler method and intuition for a similar question about an implicit 2nd order method with a demonstration of the influence of the orders of the first step.