Numerical Calculation of Invariant Tori

The problem of computing a smooth invariant manifold for a finite-dimensional dynamical system is considered. In this paper, it is assumed that the manifold can be parameterized over a torus in terms of a subset of the system variables. The approach used here then involves solving a system of partial differential equations subject to periodic boundary conditions. The resulting numerical approach is analyzed and contrasted with some previously tested ones, and several methods of implementation are considered. Numerical results are given for the forced van der Pol equation and for a system of two linearly coupled oscillators.