ly produces estimates of the solution.  And these estimates tend
      to become more inaccurate for large values of time.  Usually, we can reduce
      this error by decreasing DT and taking more, smaller time steps.
    </p>

    <p>
      In this example, for instance, taking just 100 steps gives nonsensical
      answers.  Using STEP_NUM = 1000 gives an approximate solution that seems
      to have the right kind of oscillatory behavior, except that the amplitude
      of the waves increases with each r