  A generalized Lugiato-Lefever equation is numerically solved with a
Newton-Raphson method to model Kerr frequency combs. We obtain excellent
agreement with past experiments, even for an octave-spanning comb. Simulations
are much faster than with any other technique despite including more modes than
ever before. Our study reveals that Kerr combs are associated with temporal
cavity solitons and dispersive waves, and opens up new avenues for the
understanding of Kerr comb formation.
