
    <p>
      The crossing location may be quite susceptible to the values of alpha and beta.
    </p>

    <p>
      The conservative form of the equation is
      <blockquote>
        1/2 * d(u^2)/dx = nu * d^2u/dx^2
      </blockquote>
      and this is the version we discretize.  The residual associated with node i
      is then
      <blockquote>
        f(i) = 1/2 * ( u(i+1)^2 - u(i-1)^2 / ( 2 * dx )
        - nu * ( u(i-1) - 2 * u(i) + u(i+1) ) / dx^2
      </blockquote>
      and we can apply Newto