  A Kolmogorov-type cascade of Kelvin waves--the distortion waves on vortex
lines--plays a key part in the relaxation of superfluid turbulence at low
temperatures. We propose an efficient numeric scheme for simulating the Kelvin
wave cascade on a single vortex line. The idea is likely to be generalizable
for a full-scale simulation of different regimes of superfluid turbulence. With
the new scheme, we are able to unambiguously resolve the cascade spectrum
exponent, and thus to settle the controversy between recent simulations [1] and
recently developed analytic theory [2].
  [1] W.F. Vinen, M. Tsubota and A. Mitani, Phys. Rev. Lett. 91, 135301 (2003).
  [2] E.V. Kozik and B.V. Svistunov, Phys. Rev. Lett. 92, 035301 (2004).
