Mistakes and typos that have been found so far:
Note that the correct result (the one given here) was used to generate the solid curve in Figure 5.16. Thanks to Bob Delaney for finding this and the next several errors.
! x(i,n), y(i,n) = position of particle n ! i = 1 and 2 correspond to the old and current positions
The Euler-Cromer method can be written as
where is the second derivative of y at step i. This also implies that
The Verlet method can be written as
If one eliminates from (2) one arrives at precisely (4). Hence, the two methods are equivalent with regards to y.
However, they are not necessarily the same with regards to the velocity. For the Verlet method it is best to obtain the velocity as a centered difference
which is different, and more accurate than, the Euler-Cromer expression.
Thanks to Sam Buss for pointing out the equivalence of the Euler-Cromer and Verlet methods.
Thanks to Ramin Jamshidi for finding these errors.