Exercise 5.2

In-class exercise 5.2

Verify that the procedure described in Exercise 5.1 yields the same order for the simple numerical scheme if we just omit the acceleration term completely, i.e. if our integrator looks like:

        a = acc(x, v, t);
	x += v*dt;
        v += a*dt;
        t += dt;

In other words, if the position and velocity steps are asymmetric, we are always limited by the less accurate of the two.

This ``reduced'' version of our integration scheme is often referred to as the Euler method. Its chief advantage is ease of programming, but it isn't very accurate. However, a simple change to the original scheme results in a method that is both simple and accurate, as we will see in a moment!