**Christiaan Stolk
University of Twente, Holland**

*Date:* October 26, 2005

We consider the initial value problem for a strictly
hyperbolic partial differential equation on the circle. We transform
the equation to an operator valued ODE
, where
is bounded. The transformation involves applying differential
operators, solving an elliptic differential equation, and applying a
coordinate transformation involving the characteristics, which can be
done at cost . The resulting ODE is solved using a
multiscale time-stepping method, which results in an algorithm with
complexity for the original hyperbolic equation.