Spectral methods in computing invariant tori (Q1567646)

Two new spectral implementations for computing invariant tori are presented. Although the underlying nonlinear partial differential equation is hyperbolic in nature, it has periodic boundary conditions in both space and time. The first approach uses a spatial spectral discretization and finds the solution via a shooting method. The second approach employs two-dimensional Fourier spectral discretization and uses Newton's method to find the solution. The two methods are applied to the Van der Pol oscillator and are compared with previous algorithms.