  We discuss Cahn's time cone method modeling phase transformation kinetics.
The model equation by the time cone method is an integral equation in the
space-time region. First we reduce it to a system of hyperbolic equations, and
in the case of odd spatial dimensions, the reduced system is a multiple
hyperbolic equation. Next we propose a numerical method for such a hyperbolic
system. By means of alternating direction implicit methods, numerical
simulations for practical forward problems are implemented with satisfactory
accuracy and efficiency. In particular, in the three dimensional case, our
numerical method on basis of reduced multiple hyperbolic equation, is fast.
