Exercise 5.3

In-class exercise 5.3

Repeat Exercise 5.1, but for the modified integration scheme obtained by including the "jerk" (derivative of the acceleration) term explicitly in the velocity step:

        a = acc(x, v, t);
	j = jerk(x, v, t);
	x += v*dt + 0.5*a*dt*dt;
        v += a*dt + 0.5*j*dt*dt;
        t += dt;

Note that we only include the jerk in the velocity step, for the same reason as discussed in Exercise 5.2

In simple cases (e.g. harmonic motion), the jerk may be easily obtained by differentiation. Thus, for example, if

        acc = -K * x;

then

        jerk = -K * v;

In a more complex case, we might have:

        acc = -K * sin(x);

then

        jerk = -K * cos(x) * v;

etc.

--> What is the numerically measured order of this method for the nonlinear oscillator with

        acc = -K x³

and K = 4?