Exercise 6.1

In-class exercise 6.1

Consider the long-term behavior of the energy error in the two second-order schemes we have studied. For

(1) the analytic second-order scheme and

(2) the predictor-corrector scheme,

consider the nonlinear oscillator with

        acc = -K x³

and K = 4, starting with x = 0 and v = 1 at time t = 0.

Plot the trajectory x(t) and the energy error dE = E(t) - E(0) as functions of time for dt = 0.1, for 0 <= t <= t_max = 10, 100, 1000. What do you notice about the long-term growth of the error in each scheme?